Firstly, basic concepts of graph and vertex colorings are introduced. Then, some interesting graphs with vertex colorings are presented. A vertex coloring of graph G is an assignment of colors to the vertices of G. And then by using proper vertex coloring, some interesting graphs are described. By using some applications of vertex colorings, two problems is presented interestingly. The vertex coloring is the starting point of graph coloring. The chromatic number for some interesting graphs and some results are studied. Ei Ei Moe "Application of Vertex Colorings with Some Interesting Graphs" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29263.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/29263/application-of-vertex-colorings-with-some-interesting-graphs/ei-ei-moe
This section provides an introduction to graphs and graph theory. Key points include:
- Graphs consist of vertices and edges that connect the vertices. They can be directed or undirected.
- Common terminology is introduced, such as adjacent vertices, neighborhoods, degrees of vertices, and handshaking theorem.
- Different types of graphs are discussed, including multigraphs, pseudographs, and directed graphs.
- Examples of graph models are given for computer networks, social networks, information networks, transportation networks, and software design. Graphs can be used to model many real-world systems and applications.
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relationships between objects. A graph consists of vertices and edges that connect the vertices. Graph theory is used in computer science to model problems that can be represented as networks, such as determining routes in a city or designing circuits. It allows analyzing properties of graphs like connectivity and determining the minimum number of resources required. A graph can be represented using an adjacency matrix or adjacency list to store information about its vertices and edges.
This document provides an introduction to graph theory concepts. It defines graphs as mathematical objects consisting of nodes and edges. Both directed and undirected graphs are discussed. Key graph properties like paths, cycles, degrees, and connectivity are defined. Classic graph problems introduced include Eulerian circuits, Hamiltonian circuits, spanning trees, and graph coloring. Graph theory is a fundamental area of mathematics with applications in artificial intelligence.
A perfect matching in a bipartite graph is a matching that matches all vertices. The document discusses algorithms for finding a perfect matching in regular bipartite graphs. The currently most efficient algorithm takes time O(m), where m is the number of edges and n is the number of vertices. The document improves this to O(min{m, n2.5ln n/d}) by proving a uniform sampling theorem: sampling each edge independently with probability O(n ln n/d2) results in a graph that has a perfect matching with high probability.
This document is a project report submitted by S. Manikanta in partial fulfillment of the requirements for a Master of Science degree in Mathematics. The report discusses applications of graph theory. It provides an overview of graph theory concepts such as definitions of graphs, terminology used in graph theory, different types of graphs, trees and forests, graph isomorphism and operations, walks and paths in graphs, representations of graphs using matrices, applications of graphs in areas like computer science, fingerprint recognition, security, and more. The document also includes examples and illustrations to explain various graph theory concepts.
This document defines and provides examples of different types of graphs, including finite and infinite graphs, simple graphs, complete graphs, bipartite graphs, and regular graphs. It introduces key graph terminology like vertices, edges, degrees, adjacency, and isolation. Examples are provided to illustrate concepts like the handshake theorem, determining if certain degree sequences can form graphs, and drawing regular graphs.
The document provides an introduction to graph theory. It lists prescribed and recommended books, outlines topics that will be covered including history, definitions, types of graphs, terminology, representation, subgraphs, connectivity, and applications. It notes that the Government of India designated June 10th as Graph Theory Day in recognition of the influence and importance of graph theory.
This section provides an introduction to graphs and graph theory. Key points include:
- Graphs consist of vertices and edges that connect the vertices. They can be directed or undirected.
- Common terminology is introduced, such as adjacent vertices, neighborhoods, degrees of vertices, and handshaking theorem.
- Different types of graphs are discussed, including multigraphs, pseudographs, and directed graphs.
- Examples of graph models are given for computer networks, social networks, information networks, transportation networks, and software design. Graphs can be used to model many real-world systems and applications.
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relationships between objects. A graph consists of vertices and edges that connect the vertices. Graph theory is used in computer science to model problems that can be represented as networks, such as determining routes in a city or designing circuits. It allows analyzing properties of graphs like connectivity and determining the minimum number of resources required. A graph can be represented using an adjacency matrix or adjacency list to store information about its vertices and edges.
This document provides an introduction to graph theory concepts. It defines graphs as mathematical objects consisting of nodes and edges. Both directed and undirected graphs are discussed. Key graph properties like paths, cycles, degrees, and connectivity are defined. Classic graph problems introduced include Eulerian circuits, Hamiltonian circuits, spanning trees, and graph coloring. Graph theory is a fundamental area of mathematics with applications in artificial intelligence.
A perfect matching in a bipartite graph is a matching that matches all vertices. The document discusses algorithms for finding a perfect matching in regular bipartite graphs. The currently most efficient algorithm takes time O(m), where m is the number of edges and n is the number of vertices. The document improves this to O(min{m, n2.5ln n/d}) by proving a uniform sampling theorem: sampling each edge independently with probability O(n ln n/d2) results in a graph that has a perfect matching with high probability.
This document is a project report submitted by S. Manikanta in partial fulfillment of the requirements for a Master of Science degree in Mathematics. The report discusses applications of graph theory. It provides an overview of graph theory concepts such as definitions of graphs, terminology used in graph theory, different types of graphs, trees and forests, graph isomorphism and operations, walks and paths in graphs, representations of graphs using matrices, applications of graphs in areas like computer science, fingerprint recognition, security, and more. The document also includes examples and illustrations to explain various graph theory concepts.
This document defines and provides examples of different types of graphs, including finite and infinite graphs, simple graphs, complete graphs, bipartite graphs, and regular graphs. It introduces key graph terminology like vertices, edges, degrees, adjacency, and isolation. Examples are provided to illustrate concepts like the handshake theorem, determining if certain degree sequences can form graphs, and drawing regular graphs.
The document provides an introduction to graph theory. It lists prescribed and recommended books, outlines topics that will be covered including history, definitions, types of graphs, terminology, representation, subgraphs, connectivity, and applications. It notes that the Government of India designated June 10th as Graph Theory Day in recognition of the influence and importance of graph theory.
This document provides an introduction to fundamental concepts in graph theory. It defines what a graph is composed of and different graph types including simple graphs, directed graphs, bipartite graphs, and complete graphs. It discusses graph terminology such as vertices, edges, paths, cycles, components, and subgraphs. It also covers graph properties like connectivity, degrees, isomorphism, and graph coloring. Examples are provided to illustrate key graph concepts and theorems are stated about properties of graphs like the Petersen graph and graph components.
This document provides an introduction to graphs and graph terminology. It defines what a graph is composed of, including vertices and edges. It gives examples of graphs and has the student practice identifying vertices and edges. It also introduces common graph terminology like degree of a vertex, adjacent vertices, paths, circuits, bridges, Euler paths, and Euler circuits. Fleury's algorithm for finding an Euler circuit or path in a graph is described. The document uses examples and exercises to help students learn and practice applying these graph concepts.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.Graph theory is also important in real life.
This document provides an introduction to graph theory concepts. It defines what a graph is consisting of vertices and edges. It discusses different types of graphs like simple graphs, multigraphs, digraphs and their properties. It introduces concepts like degrees of vertices, handshaking lemma, planar graphs, Euler's formula, bipartite graphs and graph coloring. It provides examples of special graphs like complete graphs, cycles, wheels and hypercubes. It discusses applications of graphs in areas like job assignments and local area networks. The document also summarizes theorems regarding planar graphs like Kuratowski's theorem stating conditions for a graph to be non-planar.
Graph theory has many applications including social networks, data organization, and communication networks. The document discusses Dijkstra's algorithm for finding the shortest path between nodes in a graph and its application to finding shortest routes between cities. It also discusses using graph representations for fingerprint classification, where fingerprints are modeled as graphs with nodes for fingerprint regions and edges between adjacent regions. Fingerprints are classified based on the structure of these graphs and compared to model graphs for matching.
The document discusses graph theory and provides definitions and examples of various graph concepts. It defines what a graph is consisting of vertices and edges. It also defines different types of graphs such as simple graphs, multigraphs, digraphs and provides examples. It discusses graph terminology, models, degree of graphs, handshaking lemma, special graphs and applications. It also provides explanations of planar graphs, Euler's formula and graph coloring.
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The document discusses various graph terminologies and special types of graphs. It defines undirected and directed graphs, and describes degrees, handshaking theorem, and other properties. Special graph types covered include complete graphs, cycles, wheels, n-cubes, and bipartite graphs. It provides examples of constructing new graphs from existing ones and an application using a bipartite graph model for employee skills and job assignments.
This document provides an overview of Lesson 17 from the NYS COMMON CORE MATHEMATICS CURRICULUM. The lesson teaches students how to draw coordinate planes and locate points on the plane given as ordered pairs. It includes 4 examples of drawing coordinate planes with different scales for the axes in order to properly display the given points. The lesson emphasizes the importance of first examining the range of values in a set of points before assigning scales to the axes.
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This is a research paper which I have conducted at the final year of undergrad study and got 4.00/4.00. It is mainly related to graph theory and has many applications in practical life.
This document provides an introduction to basic graph theory terminology and concepts. It defines a graph as a data structure consisting of nodes and edges that relate the nodes. Examples of graphs include networks, electronic circuits, and navigation systems. Classic problems in graph theory are discussed, such as the Seven Bridges of Königsberg problem solved by Euler that established graph theory. Euler's theory on Euler paths and circuits is explained along with formal definitions of graphs, vertices, edges, and examples. Terminology including adjacent vertices, endpoints, and origins of edges are also defined.
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Graphs are useful tools for modeling problems and consist of vertices and edges. Breadth-first search (BFS) is an algorithm that visits the vertices of a graph starting from a source vertex and proceeding to visit neighboring vertices first, before moving to neighbors that are further away. BFS uses a queue to efficiently traverse the graph and discover all possible paths from the source to other vertices, identifying the shortest paths in an unweighted graph. The time complexity of BFS on an adjacency list representation is O(n+m) where n is the number of vertices and m is the number of edges.
1) The document introduces basic concepts in graph theory including definitions of graphs, vertices, edges and examples.
2) It discusses some classic problems in graph theory including Euler's solving of the Seven Bridges of Königsberg problem, which helped formulate graph theory.
3) The document defines Euler paths, Euler circuits and the conditions for when a graph contains them based on the number of odd and even vertices.
Graph theory has many applications in modeling real-world networks like computer networks and chemical compounds. It studies graphs, which are collections of vertices connected by edges. A graph can be represented using an incidence matrix or adjacency list/matrix. Connectivity refers to reachability between vertices by traversing edges. The shortest path problem finds the minimum weight path between vertices in a weighted graph. Planar graphs can be drawn in a plane without edge crossings, and satisfy Euler's formula relating vertices, edges, and regions. Graph coloring assigns different colors to connected elements like vertices or edges.
The document discusses graph algorithms and graph theory concepts. It defines graphs, directed and undirected graphs, and graph terminology like vertices, edges, adjacency, paths, cycles, connectedness, and representations using adjacency lists and matrices. It also covers tree graphs and their properties.
The document provides definitions and examples related to graphs. It defines graphs, directed graphs, and terminology like vertices, edges, degrees, adjacency, and isomorphism. It discusses representations of graphs using adjacency lists and matrices. It also covers special types of graphs like trees, cycles, and bipartite graphs. Key concepts are illustrated with examples.
This document provides information about graphs and graph theory concepts. It defines what a graph is consisting of vertices and edges. It describes different types of graphs such as undirected graphs, directed graphs, multigraphs, and pseudographs. It also discusses graph representations using adjacency matrices, adjacency lists, and incidence matrices. Additionally, it covers graph properties and concepts such as degrees of vertices, connected graphs, connected components, planar graphs, graph coloring, and the five color theorem.
This document provides an introduction to fundamental concepts in graph theory. It defines what a graph is composed of and different graph types including simple graphs, directed graphs, bipartite graphs, and complete graphs. It discusses graph terminology such as vertices, edges, paths, cycles, components, and subgraphs. It also covers graph properties like connectivity, degrees, isomorphism, and graph coloring. Examples are provided to illustrate key graph concepts and theorems are stated about properties of graphs like the Petersen graph and graph components.
This document provides an introduction to graphs and graph terminology. It defines what a graph is composed of, including vertices and edges. It gives examples of graphs and has the student practice identifying vertices and edges. It also introduces common graph terminology like degree of a vertex, adjacent vertices, paths, circuits, bridges, Euler paths, and Euler circuits. Fleury's algorithm for finding an Euler circuit or path in a graph is described. The document uses examples and exercises to help students learn and practice applying these graph concepts.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.Graph theory is also important in real life.
This document provides an introduction to graph theory concepts. It defines what a graph is consisting of vertices and edges. It discusses different types of graphs like simple graphs, multigraphs, digraphs and their properties. It introduces concepts like degrees of vertices, handshaking lemma, planar graphs, Euler's formula, bipartite graphs and graph coloring. It provides examples of special graphs like complete graphs, cycles, wheels and hypercubes. It discusses applications of graphs in areas like job assignments and local area networks. The document also summarizes theorems regarding planar graphs like Kuratowski's theorem stating conditions for a graph to be non-planar.
Graph theory has many applications including social networks, data organization, and communication networks. The document discusses Dijkstra's algorithm for finding the shortest path between nodes in a graph and its application to finding shortest routes between cities. It also discusses using graph representations for fingerprint classification, where fingerprints are modeled as graphs with nodes for fingerprint regions and edges between adjacent regions. Fingerprints are classified based on the structure of these graphs and compared to model graphs for matching.
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This is a research paper which I have conducted at the final year of undergrad study and got 4.00/4.00. It is mainly related to graph theory and has many applications in practical life.
This document provides an introduction to basic graph theory terminology and concepts. It defines a graph as a data structure consisting of nodes and edges that relate the nodes. Examples of graphs include networks, electronic circuits, and navigation systems. Classic problems in graph theory are discussed, such as the Seven Bridges of Königsberg problem solved by Euler that established graph theory. Euler's theory on Euler paths and circuits is explained along with formal definitions of graphs, vertices, edges, and examples. Terminology including adjacent vertices, endpoints, and origins of edges are also defined.
This document defines and provides examples of key concepts in graph theory, including subgraphs, walks, paths, cycles, connectivity, and k-connectivity. It defines subgraphs, spanning subgraphs, trivial subgraphs, and induced subgraphs. It defines walks, paths, and cycles. It defines connectivity and connectivity in graphs, articulation vertices, bridges, and distance in connected graphs. It defines k-connectivity and cut vertices. It provides examples of separating sets, edge connectivity, edge cuts, and blocks.
Graphs are useful tools for modeling problems and consist of vertices and edges. Breadth-first search (BFS) is an algorithm that visits the vertices of a graph starting from a source vertex and proceeding to visit neighboring vertices first, before moving to neighbors that are further away. BFS uses a queue to efficiently traverse the graph and discover all possible paths from the source to other vertices, identifying the shortest paths in an unweighted graph. The time complexity of BFS on an adjacency list representation is O(n+m) where n is the number of vertices and m is the number of edges.
1) The document introduces basic concepts in graph theory including definitions of graphs, vertices, edges and examples.
2) It discusses some classic problems in graph theory including Euler's solving of the Seven Bridges of Königsberg problem, which helped formulate graph theory.
3) The document defines Euler paths, Euler circuits and the conditions for when a graph contains them based on the number of odd and even vertices.
Graph theory has many applications in modeling real-world networks like computer networks and chemical compounds. It studies graphs, which are collections of vertices connected by edges. A graph can be represented using an incidence matrix or adjacency list/matrix. Connectivity refers to reachability between vertices by traversing edges. The shortest path problem finds the minimum weight path between vertices in a weighted graph. Planar graphs can be drawn in a plane without edge crossings, and satisfy Euler's formula relating vertices, edges, and regions. Graph coloring assigns different colors to connected elements like vertices or edges.
The document discusses graph algorithms and graph theory concepts. It defines graphs, directed and undirected graphs, and graph terminology like vertices, edges, adjacency, paths, cycles, connectedness, and representations using adjacency lists and matrices. It also covers tree graphs and their properties.
The document provides definitions and examples related to graphs. It defines graphs, directed graphs, and terminology like vertices, edges, degrees, adjacency, and isomorphism. It discusses representations of graphs using adjacency lists and matrices. It also covers special types of graphs like trees, cycles, and bipartite graphs. Key concepts are illustrated with examples.
This document provides information about graphs and graph theory concepts. It defines what a graph is consisting of vertices and edges. It describes different types of graphs such as undirected graphs, directed graphs, multigraphs, and pseudographs. It also discusses graph representations using adjacency matrices, adjacency lists, and incidence matrices. Additionally, it covers graph properties and concepts such as degrees of vertices, connected graphs, connected components, planar graphs, graph coloring, and the five color theorem.
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
This document provides an introduction to graph theory, including basic terminology and concepts. It defines what a graph is mathematically as a collection of vertices and edges. It describes different types of graphs such as simple graphs, multiple graphs, weighted graphs, finite and infinite graphs, labeled graphs, and directed graphs. It also defines graph theory terms like adjacency, incidence, degree of a vertex, isomorphism, subgraphs, and graph operations like union and intersection. The document provides examples to illustrate each term and concept.
This document provides an introduction to graph theory, including basic terminology and concepts. It defines what a graph is mathematically as a collection of vertices and edges. It describes different types of graphs such as simple graphs, multiple graphs, weighted graphs, finite and infinite graphs, labeled graphs, and directed graphs. It also defines graph theory terms like adjacency, incidence, degree of a vertex, isomorphism, subgraphs, and graph operations like union and intersection. The document provides examples to illustrate each term and concept.
1) Graph theory concepts such as undirected graphs, directed graphs, weighted graphs, mixed graphs, simple graphs, multigraphs, and pseudographs are introduced. Common graph terminology like vertices, edges, loops, degrees, adjacency and connectivity are defined.
2) Different types of graphs are discussed including trees, forests, cycles, wheels, complete graphs, bipartite graphs, and n-cubes. Matrix representations using adjacency matrices are also covered.
3) The document touches on graph isomorphism, Eulerian graphs, Hamiltonian graphs, and algorithms for determining graph properties like connectivity and number of components.
1. Graph and Graph Terminologiesimp.pptxswapnilbs2728
There are five main categories of graphs: simple graphs, multigraphs, pseudographs, directed graphs, and directed multigraphs. An undirected graph G consists of a set of vertices V and a set of edges E that connect the vertices. A directed graph consists of vertices V and directed edges E that have an initial and terminal vertex. There are several special types of simple graphs including complete graphs, cycles, wheels, and bipartite graphs.
This document defines and discusses the complementary perfect triple connected domination number of a graph. It begins by introducing concepts like triple connected graphs and triple connected dominating sets. It then defines a complementary perfect triple connected dominating set as a triple connected dominating set where the induced subgraph on the remaining vertices has a perfect matching. The complementary perfect triple connected domination number is the minimum cardinality of such sets. The document determines this number for some standard graph classes and establishes bounds for general graphs, exploring relationships with other graph parameters.
This document provides an overview of key concepts in graph theory, including:
- A graph consists of a set of vertices and edges connecting pairs of vertices.
- Paths and cycles are walks through a graph without repeating edges or vertices. A tree is an acyclic connected graph.
- The degree of a vertex is the number of edges connected to it. Regular graphs have all vertices of the same degree.
- Graphs can be represented using adjacency matrices and incidence matrices to show connections between vertices and edges.
- Directed graphs have edges oriented from a starting to ending vertex. Connectedness in directed graphs depends on the underlying graph or directionality of paths.
This document defines basic concepts in graph theory. A graph consists of a set of vertices and edges connecting pairs of vertices. An adjacency matrix represents which vertices are connected by edges, while an incidence matrix represents which edges connect to each vertex. A simple graph cannot have loops or multiple edges between vertices. A complete graph connects each pair of vertices. Two graphs are isomorphic if there is a one-to-one correspondence between their vertices that preserves edge connections. Multigraphs allow multiple edges between vertices, while pseudographs also allow loops. The degree of a vertex is the number of edges connected to it.
This document provides an overview of graphs and graph algorithms. It defines graphs, directed and undirected graphs, and graph terminology like vertices, edges, paths, cycles, connected components, and degrees. It describes different graph representations like adjacency matrices and adjacency lists. It also explains graph traversal algorithms like depth-first search and breadth-first search. Finally, it covers graph algorithms for finding minimum spanning trees, shortest paths, and transitive closure.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document defines and discusses the concept of paired triple connected domination number of a graph. It begins by reviewing existing concepts like domination number, connected domination number, and triple connected domination number. It then introduces the new concept of a paired triple connected dominating set as a triple connected dominating set where the induced subgraph also has a perfect matching. The paired triple connected domination number is defined as the minimum cardinality of such a set. The document explores properties of this number and its relationship to other graph parameters. Examples are provided to illustrate the definitions.
This document discusses the concept of strong triple connected domination number (stc) of a graph. Some key points:
1. A subset S of vertices is a strong triple connected dominating set if S is a strong dominating set and the induced subgraph <S> is triple connected.
2. The strong triple connected domination number stc(G) is the minimum cardinality of a strong triple connected dominating set.
3. Some standard graphs for which the exact stc value is determined include paths, cycles, complete graphs, wheels, and more.
4. Bounds on stc(G) are established, such as 3 ≤ stc(G) ≤ p-1
The document introduces the concept of a restrained triple connected dominating set and restrained triple connected domination number (γrtc) of a graph. A restrained triple connected dominating set is a restrained dominating set where the induced subgraph is triple connected. γrtc is defined as the minimum cardinality of a restrained triple connected dominating set. Bounds on γrtc are provided for general graphs. Exact values of γrtc are given for certain standard graphs like cycles, complete graphs, and complete bipartite graphs. Properties of γrtc are explored, such as the relationship between a graph and its spanning subgraphs.
1. A graph is a collection of objects called vertices that are connected by links called edges. Graphs can be represented as a pair of sets (V,E) where V is the set of vertices and E is the set of edges.
2. There are several important terms used to describe graphs including adjacent nodes, degree of a node, regular graphs, paths, cycles, connected graphs, and complete graphs. Graphs can be represented using adjacency matrices or adjacency lists.
3. There are two main techniques for traversing graphs - depth-first search (DFS) and breadth-first search (BFS). DFS uses a stack and traverses graphs in a depth-wise manner while BFS uses a
The document discusses graphs and graph theory. It defines graphs as non-linear data structures used to model networks and relationships. The key types of graphs are undirected graphs, where edges have no orientation, and directed graphs, where edges have orientation. Graph traversal algorithms like depth-first search and breadth-first search are discussed. Common graph terminology is defined, including vertices, edges, paths, cycles, degrees. Different graph representations like adjacency matrices and adjacency lists are also covered. Applications of graphs include modeling networks, routes, and relationships.
This document provides an overview of graph theory concepts. It defines what a graph is consisting of vertices and edges. It describes different types of graphs such as directed vs undirected, simple vs complex graphs. It introduces common graph terminology like degree of a vertex, adjacent/incident vertices, and connectivity. Examples of applications are given such as transportation networks, web graphs, and scheduling problems. Special graph cases like complete graphs and cycles are also defined.
Graph algorithms can be used to model and solve many real world problems. Some famous graph problems include the traveling salesman problem of planning the shortest route to visit all cities once, and the four color theorem about coloring maps with four colors so no adjacent regions have the same color. Graphs are mathematical structures used to represent pairwise relationships between objects. They are made up of vertices connected by edges, and common graph algorithms involve finding shortest paths, matching items, or modeling flows through networks.
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph consists of vertices connected by edges. The magnitude of a graph is characterized by the number of vertices and edges. Directed graphs have edges represented as ordered pairs of vertices, while undirected graphs have edges represented as unordered vertex pairs. The degree of a vertex is the number of edges connected to it. For directed graphs, in-degree is the number of edges entering a vertex and out-degree is the number of edges leaving it. The Handshaking Theorem states that for an undirected graph, the sum of the degrees of all vertices equals twice the number of edges.
This document provides an introduction to graph theory through a presentation on the topic. It defines what a graph is by explaining that a graph G consists of a set of vertices V and edges E. It then gives examples and defines basic terminology like adjacency and incidence. The document also covers topics like degrees of vertices, regular and bipartite graphs, and representations of graphs through adjacency and incidence matrices.
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Edge computing, a paradigm that involves processing data closer to its source, has gained significant attention for its potential to revolutionize data processing and communication in space missions. With the increasing complexity and data volume generated by modern space missions, traditional centralized computing approaches face challenges related to latency, bandwidth, and security. Edge computing in space, involving on board processing and analysis of data, offers promising solutions to these challenges. This paper explores the concept of edge computing in space, its benefits, applications, and future prospects in enhancing space missions. Manish Verma "Edge Computing in Space: Enhancing Data Processing and Communication for Space Missions" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64541.pdf Paper Url: https://www.ijtsrd.com/computer-science/artificial-intelligence/64541/edge-computing-in-space-enhancing-data-processing-and-communication-for-space-missions/manish-verma
Dynamics of Communal Politics in 21st Century India Challenges and Prospectsijtsrd
Communal politics in India has evolved through centuries, weaving a complex tapestry shaped by historical legacies, colonial influences, and contemporary socio political transformations. This research comprehensively examines the dynamics of communal politics in 21st century India, emphasizing its historical roots, socio political dynamics, economic implications, challenges, and prospects for mitigation. The historical perspective unravels the intricate interplay of religious identities and power dynamics from ancient civilizations to the impact of colonial rule, providing insights into the evolution of communalism. The socio political dynamics section delves into the contemporary manifestations, exploring the roles of identity politics, socio economic disparities, and globalization. The economic implications section highlights how communal politics intersects with economic issues, perpetuating disparities and influencing resource allocation. Challenges posed by communal politics are scrutinized, revealing multifaceted issues ranging from social fragmentation to threats against democratic values. The prospects for mitigation present a multifaceted approach, incorporating policy interventions, community engagement, and educational initiatives. The paper conducts a comparative analysis with international examples, identifying common patterns such as identity politics and economic disparities. It also examines unique challenges, emphasizing Indias diverse religious landscape, historical legacy, and secular framework. Lessons for effective strategies are drawn from international experiences, offering insights into inclusive policies, interfaith dialogue, media regulation, and global cooperation. By scrutinizing historical epochs, contemporary dynamics, economic implications, and international comparisons, this research provides a comprehensive understanding of communal politics in India. The proposed strategies for mitigation underscore the importance of a holistic approach to foster social harmony, inclusivity, and democratic values. Rose Hossain "Dynamics of Communal Politics in 21st Century India: Challenges and Prospects" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64528.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/history/64528/dynamics-of-communal-politics-in-21st-century-india-challenges-and-prospects/rose-hossain
Assess Perspective and Knowledge of Healthcare Providers Towards Elehealth in...ijtsrd
Background and Objective Telehealth has become a well known tool for the delivery of health care in Saudi Arabia, and the perspective and knowledge of healthcare providers are influential in the implementation, adoption and advancement of the method. This systematic review was conducted to examine the current literature base regarding telehealth and the related healthcare professional perspective and knowledge in the Kingdom of Saudi Arabia. Materials and Methods This systematic review was conducted by searching 7 databases including, MEDLINE, CINHAL, Web of Science, Scopus, PubMed, PsycINFO, and ProQuest Central. Studies on healthcare practitioners telehealth knowledge and perspectives published in English in Saudi Arabia from 2000 to 2023 were included. Boland directed this comprehensive review. The researchers examined each connected study using the AXIS tool, which evaluates cross sectional systematic reviews. Narrative synthesis was used to summarise and convey the data. Results Out of 1840 search results, 10 studies were included. Positive outlook and limited knowledge among providers were seen across trials. Healthcare professionals like telehealth for its ability to improve quality, access, and delivery, save time and money, and be successful. Age, gender, occupation, and work experience also affect health workers knowledge. In Saudi Arabia, healthcare professionals face inadequate expert assistance, patient privacy, internet connection concerns, lack of training courses, lack of telehealth understanding, and high costs while performing telemedicine. Conclusions Healthcare practitioners telehealth perceptions and knowledge were examined in this systematic study. Its collection of concerned experts different personal attitudes and expertise would help enhance telehealths implementation in Saudi Arabia, develop its healthcare delivery alternative, and eliminate frequent problems. Badriah Mousa I Mulayhi | Dr. Jomin George | Judy Jenkins "Assess Perspective and Knowledge of Healthcare Providers Towards Elehealth in Saudi Arabia: A Systematic Review" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64535.pdf Paper Url: https://www.ijtsrd.com/medicine/other/64535/assess-perspective-and-knowledge-of-healthcare-providers-towards-elehealth-in-saudi-arabia-a-systematic-review/badriah-mousa-i-mulayhi
The Impact of Digital Media on the Decentralization of Power and the Erosion ...ijtsrd
The impact of digital media on the distribution of power and the weakening of traditional gatekeepers has gained considerable attention in recent years. The adoption of digital technologies and the internet has resulted in declining influence and power for traditional gatekeepers such as publishing houses and news organizations. Simultaneously, digital media has facilitated the emergence of new voices and players in the media industry. Digital medias impact on power decentralization and gatekeeper erosion is visible in several ways. One significant aspect is the democratization of information, which enables anyone with an internet connection to publish and share content globally, leading to citizen journalism and bypassing traditional gatekeepers. Another aspect is the disruption of conventional media industry business models, as traditional organizations struggle to adjust to the decrease in advertising revenue and the rise of digital platforms. Alternative business models, such as subscription models and crowdfunding, have become more prevalent, leading to the emergence of new players. Overall, the impact of digital media on the distribution of power and the weakening of traditional gatekeepers has brought about significant changes in the media landscape and the way information is shared. Further research is required to fully comprehend the implications of these changes and their impact on society. Dr. Kusum Lata "The Impact of Digital Media on the Decentralization of Power and the Erosion of Traditional Gatekeepers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64544.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/political-science/64544/the-impact-of-digital-media-on-the-decentralization-of-power-and-the-erosion-of-traditional-gatekeepers/dr-kusum-lata
Online Voices, Offline Impact Ambedkars Ideals and Socio Political Inclusion ...ijtsrd
This research investigates the nexus between online discussions on Dr. B.R. Ambedkars ideals and their impact on social inclusion among college students in Gurugram, Haryana. Surveying 240 students from 12 government colleges, findings indicate that 65 actively engage in online discussions, with 80 demonstrating moderate to high awareness of Ambedkars ideals. Statistically significant correlations reveal that higher online engagement correlates with increased awareness p 0.05 and perceived social inclusion. Variations across colleges and a notable effect of college type on perceived social inclusion highlight the influence of contextual factors. Furthermore, the intersectional analysis underscores nuanced differences based on gender, caste, and socio economic status. Dr. Kusum Lata "Online Voices, Offline Impact: Ambedkar's Ideals and Socio-Political Inclusion - A Study of Gurugram District" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64543.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/political-science/64543/online-voices-offline-impact-ambedkars-ideals-and-sociopolitical-inclusion--a-study-of-gurugram-district/dr-kusum-lata
Problems and Challenges of Agro Entreprenurship A Studyijtsrd
Noting calls for contextualizing Agro entrepreneurs problems and challenges of the agro entrepreneurs and for greater attention to the Role of entrepreneurs in agro entrepreneurship research, we conduct a systematic literature review of extent research in agriculture entrepreneurship to overcome the study objectives of complications of agro entrepreneurs through various factors, Development of agriculture products is a key factor for the overall economic growth of agro entrepreneurs Agro Entrepreneurs produces firsthand large scale employment, utilizes the labor and natural resources, This research outlines the problems of Weather and Soil Erosions, Market price fluctuation, stimulates labor cost problems, reduces concentration of Price volatility, Dependency on Intermediaries, induces Limited Bargaining Power, and Storage and Transportation Costs. This paper mainly devoted to highlight Problems and challenges faced for the sustainable of Agro Entrepreneurs in India. Vinay Prasad B "Problems and Challenges of Agro Entreprenurship - A Study" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64540.pdf Paper Url: https://www.ijtsrd.com/other-scientific-research-area/other/64540/problems-and-challenges-of-agro-entreprenurship--a-study/vinay-prasad-b
Comparative Analysis of Total Corporate Disclosure of Selected IT Companies o...ijtsrd
Disclosure is a process through which a business enterprise communicates with external parties. A corporate disclosure is communication of financial and non financial information of the activities of a business enterprise to the interested entities. Corporate disclosure is done through publishing annual reports. So corporate disclosure through annual reports plays a vital role in the life of all the companies and provides valuable information to investors. The basic objectives of corporate disclosure is to give a true and fair view of companies to the parties related either directly or indirectly like owner, government, creditors, shareholders etc. in the companies act, provisions have been made about mandatory and voluntary disclosure. The IT sector in India is rapidly growing, the trend to invest in the IT sector is rising and employment opportunities in IT sectors are also increasing. Therefore the IT sector is expected to have fair, full and adequate disclosure of all information. Unfair and incomplete disclosure may adversely affect the entire economy. A research study on disclosure practices of IT companies could play an important role in this regard. Hence, the present research study has been done to study and review comparative analysis of total corporate disclosure of selected IT companies of India and to put forward overall findings and suggestions with a view to increase disclosure score of these companies. The researcher hopes that the present research study will be helpful to all selected Companies for improving level of corporate disclosure through annual reports as well as the government, creditors, investors, all business organizations and upcoming researcher for comparative analyses of level of corporate disclosure with special reference to selected IT companies. Dr. Vaibhavi D. Thaker "Comparative Analysis of Total Corporate Disclosure of Selected IT Companies of India" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64539.pdf Paper Url: https://www.ijtsrd.com/other-scientific-research-area/other/64539/comparative-analysis-of-total-corporate-disclosure-of-selected-it-companies-of-india/dr-vaibhavi-d-thaker
The Impact of Educational Background and Professional Training on Human Right...ijtsrd
This study investigated the impact of educational background and professional training on human rights awareness among secondary school teachers in the Marathwada region of Maharashtra, India. The key findings reveal that higher levels of education, particularly a master’s degree, and fields of study related to education, humanities, or social sciences are associated with greater human rights awareness among teachers. Additionally, both pre service teacher training and in service professional development programs focused on human rights education significantly enhance teacher’s knowledge, skills, and competencies in promoting human rights principles in their classrooms. Baig Ameer Bee Mirza Abdul Aziz | Dr. Syed Azaz Ali Amjad Ali "The Impact of Educational Background and Professional Training on Human Rights Awareness among Secondary School Teachers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64529.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/education/64529/the-impact-of-educational-background-and-professional-training-on-human-rights-awareness-among-secondary-school-teachers/baig-ameer-bee-mirza-abdul-aziz
A Study on the Effective Teaching Learning Process in English Curriculum at t...ijtsrd
“One Language sets you in a corridor for life. Two languages open every door along the way” Frank Smith English as a foreign language or as a second language has been ruling in India since the period of Lord Macaulay. But the question is how much we teach or learn English properly in our culture. Is there any scope to use English as a language rather than a subject How much we learn or teach English without any interference of mother language specially in the classroom teaching learning scenario in West Bengal By considering all these issues the researcher has attempted in this article to focus on the effective teaching learning process comparing to other traditional strategies in the field of English curriculum at the secondary level to investigate whether they fulfill the present teaching learning requirements or not by examining the validity of the present curriculum of English. The purpose of this study is to focus on the effectiveness of the systematic, scientific, sequential and logical transaction of the course between the teachers and the learners in the perspective of the 5Es programme that is engage, explore, explain, extend and evaluate. Sanchali Mondal | Santinath Sarkar "A Study on the Effective Teaching Learning Process in English Curriculum at the Secondary Level of West Bengal" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd62412.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/education/62412/a-study-on-the-effective-teaching-learning-process-in-english-curriculum-at-the-secondary-level-of-west-bengal/sanchali-mondal
The Role of Mentoring and Its Influence on the Effectiveness of the Teaching ...ijtsrd
This paper reports on a study which was conducted to investigate the role of mentoring and its influence on the effectiveness of the teaching of Physics in secondary schools in the South West Region of Cameroon. The study adopted the convergent parallel mixed methods design, focusing on respondents in secondary schools in the South West Region of Cameroon. Both quantitative and qualitative data were collected, analysed separately, and the results were compared to see if the findings confirm or disconfirm each other. The quantitative analysis found that majority of the respondents 72 of Physics teachers affirmed that they had more experienced colleagues as mentors to help build their confidence, improve their teaching, and help them improve their effectiveness and efficiency in guiding learners’ achievements. Only 28 of the respondents disagreed with these statements. With majority respondents 72 agreeing with the statements, it implies that in most secondary schools, experienced Physics teachers act as mentors to build teachers’ confidence in teaching and improving students’ learning. The interview qualitative data analysis summarized how secondary school Principals use meetings with mentors and mentees to promote mentorship in the school milieu. This has helped strengthen teachers’ classroom practices in secondary schools in the South West Region of Cameroon. With the results confirming each other, the study recommends that mentoring should focus on helping teachers employ social interactions and instructional practices feedback and clarity in teaching that have direct measurable impact on students’ learning achievements. Andrew Ngeim Sumba | Frederick Ebot Ashu | Peter Agborbechem Tambi "The Role of Mentoring and Its Influence on the Effectiveness of the Teaching of Physics in Secondary Schools in the South West Region of Cameroon" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64524.pdf Paper Url: https://www.ijtsrd.com/management/management-development/64524/the-role-of-mentoring-and-its-influence-on-the-effectiveness-of-the-teaching-of-physics-in-secondary-schools-in-the-south-west-region-of-cameroon/andrew-ngeim-sumba
Design Simulation and Hardware Construction of an Arduino Microcontroller Bas...ijtsrd
This study primarily focuses on the design of a high side buck converter using an Arduino microcontroller. The converter is specifically intended for use in DC DC applications, particularly in standalone solar PV systems where the PV output voltage exceeds the load or battery voltage. To evaluate the performance of the converter, simulation experiments are conducted using Proteus Software. These simulations provide insights into the input and output voltages, currents, powers, and efficiency under different state of charge SoC conditions of a 12V,70Ah rechargeable lead acid battery. Additionally, the hardware design of the converter is implemented, and practical data is collected through operation, monitoring, and recording. By comparing the simulation results with the practical results, the efficiency and performance of the designed converter are assessed. The findings indicate that while the buck converter is suitable for practical use in standalone PV systems, its efficiency is compromised due to a lower output current. Chan Myae Aung | Dr. Ei Mon "Design Simulation and Hardware Construction of an Arduino-Microcontroller Based DC-DC High-Side Buck Converter for Standalone PV System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64518.pdf Paper Url: https://www.ijtsrd.com/engineering/mechanical-engineering/64518/design-simulation-and-hardware-construction-of-an-arduinomicrocontroller-based-dcdc-highside-buck-converter-for-standalone-pv-system/chan-myae-aung
Sustainable Energy by Paul A. Adekunte | Matthew N. O. Sadiku | Janet O. Sadikuijtsrd
Energy becomes sustainable if it meets the needs of the present without compromising the ability of future generations to meet their own needs. Some of the definitions of sustainable energy include the considerations of environmental aspects such as greenhouse gas emissions, social, and economic aspects such as energy poverty. Generally far more sustainable than fossil fuel are renewable energy sources such as wind, hydroelectric power, solar, and geothermal energy sources. Worthy of note is that some renewable energy projects, like the clearing of forests to produce biofuels, can cause severe environmental damage. The sustainability of nuclear power which is a low carbon source is highly debated because of concerns about radioactive waste, nuclear proliferation, and accidents. The switching from coal to natural gas has environmental benefits, including a lower climate impact, but could lead to delay in switching to more sustainable options. “Carbon capture and storage” can be built into power plants to remove the carbon dioxide CO2 emissions, but this technology is expensive and has rarely been implemented. Leading non renewable energy sources around the world is fossil fuels, coal, petroleum, and natural gas. Nuclear energy is usually considered another non renewable energy source, although nuclear energy itself is a renewable energy source, but the material used in nuclear power plants is not. The paper addresses the issue of sustainable energy, its attendant benefits to the future generation, and humanity in general. Paul A. Adekunte | Matthew N. O. Sadiku | Janet O. Sadiku "Sustainable Energy" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64534.pdf Paper Url: https://www.ijtsrd.com/engineering/electrical-engineering/64534/sustainable-energy/paul-a-adekunte
Concepts for Sudan Survey Act Implementations Executive Regulations and Stand...ijtsrd
This paper aims to outline the executive regulations, survey standards, and specifications required for the implementation of the Sudan Survey Act, and for regulating and organizing all surveying work activities in Sudan. The act has been discussed for more than 5 years. The Land Survey Act was initiated by the Sudan Survey Authority and all official legislations were headed by the Sudan Ministry of Justice till it was issued in 2022. The paper presents conceptual guidelines to be used for the Survey Act implementation and to regulate the survey work practice, standardizing the field surveys, processing, quality control, procedures, and the processes related to survey work carried out by the stakeholders and relevant authorities in Sudan. The conceptual guidelines are meant to improve the quality and harmonization of geospatial data and to aid decision making processes as well as geospatial information systems. The established comprehensive executive regulations will govern and regulate the implementation of the Sudan Survey Geomatics Act in all surveying and mapping practices undertaken by the Sudan Survey Authority SSA and state local survey departments for public or private sector organizations. The targeted standards and specifications include the reference frame, projection, coordinate systems, and the guidelines and specifications that must be followed in the field of survey work, processes, and mapping products. In the last few decades, there has been a growing awareness of the importance of geomatics activities and measurements on the Earths surface in space and time, together with observing and mapping the changes. In such cases, data must be captured promptly, standardized, and obtained with more accuracy and specified in much detail. The paper will also highlight the current situation in Sudan, the degree to which survey standards are used, the problems encountered, and the errors that arise from not using the standards and survey specifications. Kamal A. A. Sami "Concepts for Sudan Survey Act Implementations - Executive Regulations and Standards" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63484.pdf Paper Url: https://www.ijtsrd.com/engineering/civil-engineering/63484/concepts-for-sudan-survey-act-implementations--executive-regulations-and-standards/kamal-a-a-sami
Towards the Implementation of the Sudan Interpolated Geoid Model Khartoum Sta...ijtsrd
The discussions between ellipsoid and geoid have invoked many researchers during the recent decades, especially during the GNSS technology era, which had witnessed a great deal of development but still geoid undulation requires more investigations. To figure out a solution for Sudans local geoid, this research has tried to intake the possibility of determining the geoid model by following two approaches, gravimetric and geometrical geoid model determination, by making use of GNSS leveling benchmarks at Khartoum state. The Benchmarks are well distributed in the study area, in which, the horizontal coordinates and the height above the ellipsoid have been observed by GNSS while orthometric heights were carried out using precise leveling. The Global Geopotential Model GGM represented in EGM2008 has been exploited to figure out the geoid undulation at the benchmarks in the study area. This is followed by a fitting process, that has been done to suit the geoid undulation data which has been computed using GNSS leveling data and geoid undulation inspired by the EGM2008. Two geoid surfaces were created after the fitting process to ensure that they are identical and both of them could be counted for getting the same geoid undulation with an acceptable accuracy. In this respect, statistical operation played an important role in ensuring the consistency and integrity of the model by applying cross validation techniques splitting the data into training and testing datasets for building the geoid model and testing its eligibility. The geometrical solution for geoid undulation computation has been utilized by applying straightforward equations that facilitate the calculation of the geoid undulation directly through applying statistical techniques for the GNSS leveling data of the study area to get the common equation parameters values that could be utilized to calculate geoid undulation of any position in the study area within the claimed accuracy. Both systems were checked and proved eligible to be used within the study area with acceptable accuracy which may contribute to solving the geoid undulation problem in the Khartoum area, and be further generalized to determine the geoid model over the entire country, and this could be considered in the future, for regional and continental geoid model. Ahmed M. A. Mohammed. | Kamal A. A. Sami "Towards the Implementation of the Sudan Interpolated Geoid Model (Khartoum State Case Study)" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63483.pdf Paper Url: https://www.ijtsrd.com/engineering/civil-engineering/63483/towards-the-implementation-of-the-sudan-interpolated-geoid-model-khartoum-state-case-study/ahmed-m-a-mohammed
Activating Geospatial Information for Sudans Sustainable Investment Mapijtsrd
Sudan is witnessing an acceleration in the processes of development and transformation in the performance of government institutions to raise the productivity and investment efficiency of the government sector. The development plans and investment opportunities have focused on achieving national goals in various sectors. This paper aims to illuminate the path to the future and provide geospatial data and information to develop the investment climate and environment for all sized businesses, and to bridge the development gap between the Sudan states. The Sudan Survey Authority SSA is the main advisor to the Sudan Government in conducting surveying, mappings, designing, and developing systems related to geospatial data and information. In recent years, SSA made a strategic partnership with the Ministry of Investment to activate Geospatial Information for Sudans Sustainable Investment and in particular, for the preparation and implementation of the Sudan investment map, based on the directives and objectives of the Ministry of Investment MI in Sudan. This paper comes within the framework of activating the efforts of the Ministry of Investment to develop technical investment services by applying techniques adopted by the Ministry and its strategic partners for advancing investment processes in the country. Kamal A. A. Sami "Activating Geospatial Information for Sudan's Sustainable Investment Map" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63482.pdf Paper Url: https://www.ijtsrd.com/engineering/information-technology/63482/activating-geospatial-information-for-sudans-sustainable-investment-map/kamal-a-a-sami
Educational Unity Embracing Diversity for a Stronger Societyijtsrd
In a rapidly changing global landscape, the importance of education as a unifying force cannot be overstated. This paper explores the crucial role of educational unity in fostering a stronger and more inclusive society through the embrace of diversity. By examining the benefits of diverse learning environments, the paper aims to highlight the positive impact on societal strength. The discussion encompasses various dimensions, from curriculum design to classroom dynamics, and emphasizes the need for educational institutions to become catalysts for unity in diversity. It highlights the need for a paradigm shift in educational policies, curricula, and pedagogical approaches to ensure that they are reflective of the diverse fabric of society. This paper also addresses the challenges associated with implementing inclusive educational practices and offers practical strategies for overcoming barriers. It advocates for collaborative efforts between educational institutions, policymakers, and communities to create a supportive ecosystem that promotes diversity and unity. Mr. Amit Adhikari | Madhumita Teli | Gopal Adhikari "Educational Unity: Embracing Diversity for a Stronger Society" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64525.pdf Paper Url: https://www.ijtsrd.com/humanities-and-the-arts/education/64525/educational-unity-embracing-diversity-for-a-stronger-society/mr-amit-adhikari
Integration of Indian Indigenous Knowledge System in Management Prospects and...ijtsrd
The diversity of indigenous knowledge systems in India is vast and can vary significantly between different communities and regions. Preserving and respecting these knowledge systems is crucial for maintaining cultural heritage, promoting sustainable practices, and fostering cross cultural understanding. In this paper, an overview of the prospects and challenges associated with incorporating Indian indigenous knowledge into management is explored. It is found that IIKS helps in management in many areas like sustainable development, tourism, food security, natural resource management, cultural preservation and innovation, etc. However, IIKS integration with management faces some challenges in the form of a lack of documentation, cultural sensitivity, language barriers legal framework, etc. Savita Lathwal "Integration of Indian Indigenous Knowledge System in Management: Prospects and Challenges" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63500.pdf Paper Url: https://www.ijtsrd.com/management/accounting-and-finance/63500/integration-of-indian-indigenous-knowledge-system-in-management-prospects-and-challenges/savita-lathwal
DeepMask Transforming Face Mask Identification for Better Pandemic Control in...ijtsrd
The COVID 19 pandemic has highlighted the crucial need of preventive measures, with widespread use of face masks being a key method for slowing the viruss spread. This research investigates face mask identification using deep learning as a technological solution to be reducing the risk of coronavirus transmission. The proposed method uses state of the art convolutional neural networks CNNs and transfer learning to automatically recognize persons who are not wearing masks in a variety of circumstances. We discuss how this strategy improves public health and safety by providing an efficient manner of enforcing mask wearing standards. The report also discusses the obstacles, ethical concerns, and prospective applications of face mask detection systems in the ongoing fight against the pandemic. Dilip Kumar Sharma | Aaditya Yadav "DeepMask: Transforming Face Mask Identification for Better Pandemic Control in the COVID-19 Era" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd64522.pdf Paper Url: https://www.ijtsrd.com/engineering/electronics-and-communication-engineering/64522/deepmask-transforming-face-mask-identification-for-better-pandemic-control-in-the-covid19-era/dilip-kumar-sharma
Streamlining Data Collection eCRF Design and Machine Learningijtsrd
Efficient and accurate data collection is paramount in clinical trials, and the design of Electronic Case Report Forms eCRFs plays a pivotal role in streamlining this process. This paper explores the integration of machine learning techniques in the design and implementation of eCRFs to enhance data collection efficiency. We delve into the synergies between eCRF design principles and machine learning algorithms, aiming to optimize data quality, reduce errors, and expedite the overall data collection process. The application of machine learning in eCRF design brings forth innovative approaches to data validation, anomaly detection, and real time adaptability. This paper discusses the benefits, challenges, and future prospects of leveraging machine learning in eCRF design for streamlined and advanced data collection in clinical trials. Dhanalakshmi D | Vijaya Lakshmi Kannareddy "Streamlining Data Collection: eCRF Design and Machine Learning" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-8 | Issue-1 , February 2024, URL: https://www.ijtsrd.com/papers/ijtsrd63515.pdf Paper Url: https://www.ijtsrd.com/biological-science/biotechnology/63515/streamlining-data-collection-ecrf-design-and-machine-learning/dhanalakshmi-d
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
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different colors. A graph is said to be vertex k-colorable if
it has a proper vertex k- coloring.
E. Chromatic Number
The vertex chromatic number of G, denoted by, is the
minimum number different colors required for a proper
vertex- coloring of G.
F. Simple Graph
A graph which has neither loops nor multiple edges. i.e,
where each edge connects two distinct vertices and no two
edges connect the same pair of vertices is called a simple
graph.
G. Example
A simple graph G and its coloring are shown in Figure
1(a) and 1(b).
Fig. 1(a) the Simple Graph G
Fig. 1(b) Coloring of the Simple Graph G
H. Example
The graph G by using proper vertex 4- coloring is shown in
figure.
Fig.2 A Proper Vertex 4-coloring of a Graph G
I. Example
We can find the chromatic number of the graph G. Coloring
of the graph G with the chromatic number 3 is shown in
figure.
Fig.3 Coloring of the Graph G with the Chromatic
Number = 3
III. SOME INTERESTING GRAPH AND COLORING OF
GRAPHS
The planar graph and by using proper vertex coloring,
some interesting graphs are described in the following.
A. Definitions
Let G = (V, E) be a graph. A planar embedding of G is a
picture of G in the plane such that the curves or line
segments that represent edges intersect only at their
endpoints. A graph that has a plane embedding is called a
planar graph.
B. Example
The planar graph and the planar embedding of graph are
shown in figure.
Fig. 4(a) A Planar Graph Fig. 4(b) A Planar
Embedding of G
C. Definitions
Region of a planar embedding of a graph is a maximal
connected portion of the plane that remains when the
curves, line segments, and points representing the graph
are removed.
Unbounded Region in the planar embedding of a graph is
the one region that contains points arbitrary far away
from the graph.
A component of G is a maximal connected sub graph of G.
D. Induced Sub graph
For any set S of vertices of G, the induced sub graph 〈ࡿ〉 is
the maximal subgraph of G with vertex set S. Thus two
vertices of S are adjacent in 〈ܵ〉 if and only if if they are
adjacent in G.
E. Theorem
Every planar graph is 6 colorable.
Proof
We prove the theorem by induction on the number of
vertices, the result being trivial for planar graphs with
fewer than seven vertices. Suppose then that G is a planar
graph with n vertices, and that all planar graphs with n-1
vertices are 6-colorable. Without loss of generality G can
be assumed to be a simple graph, and so, by Lemma (If G is
a planar graph, then G contains a vertex whose degree is at
most 5) contains a vertex v whose degree is at most 5; if
we delete v, then the graph which remains has n-1 vertices
and is that 6-colorable. A 6-coloring for G is then obtained
by coloring v with a different color from the (at most 5)
vertices adjacent to v.
F. Bipartite Graph
A graph G = (V, E) is bipartite if V can be partitioned into
two subsets ܸଵand ܸଶ(i.e, V = ܸଵ ∪ ܸଶ and ܸଵ ∩ ܸଶ ൌ ∅),
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such that every edges ݁ ∈ ܧ joins a vertex in ܸଵ and a
vertex in ܸଶ.
G. Example
The bipartite graph is shown in figure.
Fig. 5 the Bipartite Graph
H. Theorem
The graph is bipartite if and only if its chromatic number is
at most 2.
Proof
If the graph G is bipartite, with parts ܸଵ and ܸଶ, then a
coloring of G can be obtained by assigning red to each
vertex in ܸଵ and blue to each vertex in ܸଶ. Since there is no
edge from any vertex in ܸଵ to any other vertex in ܸଵ, and
no edge from any vertex in ܸଶ to any other vertex in ܸଶ, no
two adjacent vertices can receive the same color.
Therefore, the chromatic number of bipartite graph is at
most 2.
Conversely, if we have a 2-coloring of a graph G, let ܸଵ be
the set of vertices that receive color 1 and let ܸଶ be the set
of vertices that receive color 2. Since adjacent vertices
must receive different colors, there is no edge between
any two vertices in the same part. Thus, the graph is
bipartite.
I. Example
A coloring of bipartite graph with two colors is displayed
in Figure.
Fig. 6 Coloring of Bipartite Graph
J. Complete Graph
The complete graph on n vertices, for n ≥ 1, which we
denote ܭ, is a graph with n vertices and an edge joining
every pair of distinct vertices.
K. Example
The complete graph is shown in figure.
Fig. 7 the Complete Graph
L. Example
We can find the chromatic number of ܭ. A coloring of ܭ
can be constructed using n colors by assigning a different
color to each vertex. No two vertices can be assigned the
same color, since every two vertices of this graph are
adjacent. Hence, the chromatic number of ܭ ൌ ݊.
M. Example
A coloring of ܭହusing five colors is shown in Figure.
Fig. 8 A Coloring of ࡷ.
N. Complete Bipartite Graph
The complete bipartite graph ܭ,, where m and n are
positive integers, is the graph whose vertex set is the
union V= ܸଵ ∪ ܸଶ of disjoint sets of cardinalities m and n,
respectively, and whose edge set is ሼݑ|ݒݑ ∈ ܸଵ, ݒ ∈ ܸଶሽ.
Fig.9The Complete Bipartite Graph
O. Example
A coloring of ܭଷ,ସ with two colors is displayed in Figure.
Fig. 10 a Coloring of ࡷ,
P. Example
We can find the chromatic number of complete bipartite
graph K୫,୬ , where m and n are positive integers. The
number of colors needed may seem to depend on m and n.
However, only two colors are needed. Color the set of m
vertices with one color and the set of n vertices with a
second color. Since edges connect only a vertex from the
set of m vertices and a vertex from the set of n vertices, no
two adjacent vertices have the same color.
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Q. Definition
The n- cycle, for ݊ ≥3, denoted ܥ, is the graph with n
vertices, ݒଵ , ݒଶ, … , ݒ,and edge set
E=ሼݒଵݒଶ, ݒଶݒଷ, … , ݒିଵݒ, ݒݒଵሽ.
R. Example
A coloring of C6 using two colors is shown in Figure 11.
Fig. 11 A Coloring of C 6
A coloring of C5 using three colors is shown in Figure 12.
Fig. 12 a coloring of C5
S. Theorem
The chromatic number of the n- cycle is given by
( )
=
=
=
oddn
evenn
n ,3
,2
Cχ
.
Proof
Let n be even. Pick a vertex and color it red. Proceed
around the graph in a clockwise direction (using a planar
representation of the graph) coloring the second vertex
blue, the third vertex red, and so on. We observe that odd
number vertices are colored with red. Since n is even, (n-
1) is odd, Thus (n-1)st vertex is colored by red. The nth
vertex can be colored blue, since it is adjacent to the first
vertex and (n-1)st vertex. Hence, the chromatic number of
Cn is 2 when n is even.
Let n be odd. Since n is odd, (n-1) is even. For the vertices
of first to (n-1)st, we need only two colors. By first part,
we see that the color of first vertex and (n-1)st vertex are
not the same. The nth vertex is adjacent to two vertices of
different colors, namely, the first and (n-1)st. Hence, we
need third color for nth vertex. Thus, the chromatic
number of Cn is 3 when n is odd and n>1.
T. Theorem
A graph is 2-colorable if and only if it has no odd cycles.
Proof
If G has an odd cycle, then clearly it is not 2- colorable.
Suppose then that G has no odd cycle. Choose any vertex v
and partition V into two sets VandV 21 as follows,
}{ evenisvudVuV ),(:1
∈=
}{ oddisvudVuV ),(:2 ∈=
Coloring the vertices in V1 by one color and the vertices in
V2 by another color defines a 2- coloring as long as there
are no adjacent vertices within either V1 or V2. Since G has
no odd cycle, there cannot be adjacent vertices within V1
or V2.
U. Definitions
The n-spoked wheel, for ݊ ≥3, denoted ܹ, is a graph
obtained from n-cycle by adding a new vertex and edges
joining it to all the vertices of the n- cycle; the new edges
are called the spokes of the wheel.
V. Example
A coloring of six-spoked wheel using three colors is shown
in Figure.
Fig. 13 A Coloring of ࢃ
W. Example
A coloring of five- spoked wheel using four colors is shown
in Figure.
Fig. 14 A Coloring of ࢃ
X. Proposition
Wheel graphs with an even number of ‘spoke’ can be 3-
colored, while wheels with an odd number of ‘spoke’
require four colors.
Y. Theorem
If G is a graph whose largest vertex- degree is then G is
(ߩ + 1)-colorable.
Proof
The proof is by induction on the number of vertices of G.
Let G be a graph with n vertices; then if we delete any
vertex v (and the edges incident to it), the graph which
remains is a graph with n-1 vertices whose largest vertex–
degree is at most ߩ. By our induction hypothesis, this
graph is (ߩ + 1)-colorable; a (ߩ + 1)- coloring for G is then
obtained by coloring v with a different color from the (at
most ߩ) vertices adjacent to v.
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IV. SOME APPLICATIONS OF VERTEX COLORINGS
The followings are some applications of vertex colorings.
A. Example
Suppose that Mg Aung, Mg Ba, Mg Chit, Mg Hla, Mg Kyaw,
Mg Lin and Mg Tin are planning a ball. Mg Aung, Mg Chit,
Mg Hla constitute the publicity committee. Mg Chit, Mg Hla
and Mg Lin are the refreshment committee. Mg Lin and Mg
Aung make up the facilities committee. Mg Ba, Mg Chit, Mg
Hla, and Mg Kyaw form the decorations committee. Mg
Kyaw, Mg Aung, and Mg Tin are the music committee. Mg
Kyaw, Mg Lin, Mg Chit form the cleanup committee. We
can find the number of meeting times, in order for each
committee to meet once.
We will construct a graph model with one vertex for each
committee. Each vertex is labeled with the first letter of
the name of the committee that is represents. Two vertices
are adjacent whenever the committees have at least one
member in common. For example, P is adjacent to R, since
Mg Chit is on both the publicity committee and the
refreshment committee.
Fig. 15(a) Graph Model for the Ball Committee
Problem
To solve this problem, we have to find the chromatic
number of G. Each of the four vertices P, D, M, and C is
adjacent to each of the other. Thus in any coloring of G
these four vertices must receive different colors say 1, 2, 3
and 4, respectively, as shown in Figure. Now R is adjacent
to all of these except M, so it cannot receive the colors 1, 2,
or 4. Similarly, vertex F cannot receive colors 1, 3, and 4,
nor can it receive the color that R receives. But we could
color R with color 3 and F with color 2.
Fig. 15(b) Using a Coloring to Ball Committee Problem
This completes a 4-coloring of G. Since the chromatic
number of this graph is 4, four meeting times are required.
The publicity committee meets in the first time slot, the
facilities committee and the decoration committee meets
in the second time slot, refreshment and music committee
meet in the third time slot, and the cleanup committee
meets last.
B. Example
We can find a schedule of the final exams for Math 115,
Math 116, Math 185, Math 195, CS 101, CS 102, CS 273,
and CS 473, using the fewest number of different time
slots, if there are no students taking both Math 115 and CS
473, both Math 116 and CS 473, both Math 195 and CS
101, both Math 195 and CS 102, both Math 115 and Math
116, both Math 115 and Math 185, and Math 185 and Math
195, but there are students in every other combination of
courses. This scheduling problem can be solved using a
graph model, with vertices representing courses and with
an edge between two vertices if there is a common student
in the courses they represent. Each time slot for a final
exam is represented by a different color. A scheduling of
the exams corresponds to a coloring of the associated
graph.
Fig. 16(a) The Graph Representing the Scheduling of
Final Exams
Fig. 16(b) Using a Coloring to Schedule Final Exams
Time Period Courses
I Math116, CS 473
II Math 115, Math 185
III Math 195, CS 102
IV CS 101
V CS 273
SinceሼMath 116, Math 185, CS 101, CS 102, CS 273ሽ, from a
complete sub graph of G, ( )Gχ ≥ 5. Thus five time slots
are needed. A coloring of the graph using five colors and
the associated schedule are shown in Fig. 16(b).
V. CONCLUSIONS
In conclusion, by using vertex colorings, we can find
meeting time slot, Schedules for exams, the Channel
Assignment Problem with the corresponding graph
models. In Graph Theory, graph coloring is a special case
of Graph labeling (Calculable problems that satisfy a
numerical condition), assignment of colors to certain
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objects in a graph subject to certain constraints vertex
coloring, edge coloring and face coloring. One of them,
vertex coloring is presented. Vertex coloring is used in a
wide variety of scientific and engineering problems.
Therefore I will continue to study other interesting graphs
and graph coloring.
ACKNOWLEDGMENT
I wish to express my grateful thanks to Head and Associate
Professor Dr. Ngwe Kyar Su Khaing , Associate Professor
Dr. Soe Soe Kyaw and Lecturer Daw Khin Aye Tint, of
Department of Engineering Mathematics, Technological
University (Yamethin), for their hearty attention, advice
and encouragement. I specially thank my parent. I would
like to thank all the teaching staffs of the Department of
Engineering Mathematics, TU (Yamethin) for their care
and supports. I express my sincere thanks to all.
REFERENCES
[1] M., Skandera, Introduction to Combinatorics and
Graph Theory, Oxford University Press, Oxford
(2003).
[2] F. Harary, Graph Theory, Narosa Publishing House,
New Delhi(2000)
[3] R. Diestel, Graph Theory, Electronic Edition New
York (2000).
[4] R. J., Wilson, Introduction to Graph Theory, Longman
Graph Limited, London (1979).
[5] J. A. Bondy. U. S. R., Graph Theory with Applications,
Macmillan Press Ltd., London (1976).
[6] K. R. Parthasarathy, Basic Graph Theory, Mc Graw-
Hill, New Delhi (1994).