Table of Contents-.pptx
•Download as PPTX, PDF•
0 likes•3 views
This document provides an introduction and definitions for fundamental concepts in graph theory, including isomorphism, subgraphs, walks, and paths. Isomorphism refers to two graphs being identical in structure with a one-to-one correspondence between vertices and edges. A subgraph is a subset of vertices and edges from a larger graph where each edge in the subgraph connects the same endpoints. Walks are sequences of edges and vertices, while paths specifically refer to sequences where each consecutive edge shares an endpoint vertex and no vertex is repeated.
Report
Share
Report
Share
Recommended
Vanmathy no sql
Element of graph four types vertex edge path loop operation of graph three type union of graph intersection of graph graph traversal
VANU no sql ppt.pptx
The document discusses elements and operations related to graphs. It defines key graph elements like vertices, edges, loops, and degrees of vertices. It also describes operations on graphs such as finding paths and circuits, determining connectivity, and extracting subgraphs. Various graph types and conversions between directed and undirected graphs are also covered.
DATA STRUCTURE PRESENTATION.pptx
This presentation summarizes key concepts about graphs. It defines a graph as a pair of sets (V,E) where V is the set of vertices and E is the set of edges. It discusses types of graphs like simple graphs and connected graphs. It also defines important graph concepts such as subgraphs, walks, Euler paths and circuits, and shortest path problems. The presentation was delivered to lecturers in the Computer Science department on the topic of graphs.
Graphs
A basic tutorial on the elementary graph theory and its implementations using data structures.
This tutorial deals with implementation of graphs in programs using data structures ,traversal algorithms: BFS, DFS, minimal spanning trees, Kruskal's algorithm, Prim's algorithm, Shortest path problem: Dijkastra's algorithm with graphical features.
DIGITAL TEXT BOOK
The document discusses various distance metrics that can be defined on the vertices of graphs. It defines shortest path distance (also called geodesic distance) as the length of the shortest path between two vertices, which satisfies the properties of a metric. Minimum weighted path distance is defined similarly for weighted graphs. The graph diameter is defined as the maximum shortest path distance between any two vertices of a connected graph. It provides examples to illustrate these distance concepts on graphs.
Magtibay buk bind#2
The document discusses Hamiltonian graphs, which are graphs that contain a Hamiltonian circuit or path. A Hamiltonian circuit visits each vertex in the graph exactly once and forms a cycle. The document provides an example of a graph that is Hamiltonian but not Eulerian, and vice versa. It notes that while it is clear only connected graphs can be Hamiltonian, there is no simple criterion to determine if a graph is Hamiltonian like there is for Eulerian graphs. It presents Dirac's sufficient condition for a graph to be Hamiltonian.
A glimpse to topological graph theory
This document provides an introduction to topological graph theory. It begins with definitions of basic graph theory concepts from a topological perspective, such as representing graphs with curved arcs instead of straight lines. It then discusses graph drawings, incidence matrices, vertex valence, and graph maps/isomorphisms. Important classes of graphs are introduced, such as trees, paths, cycles, and complete graphs. The document aims to introduce preliminary concepts of topological graph theory to students in a simple manner.
Graph applications chapter
This document summarizes algorithms for finding connected components, topological sorting of directed acyclic graphs (DAGs), and finding minimal spanning trees in weighted undirected graphs. It describes:
1) Using breadth-first or depth-first search to find the connected components of an undirected graph by traversing from each unvisited vertex.
2) Topological sorting of DAGs by recursively traversing vertices in depth-first order and listing them in the order they are finished.
3) Kruskal's algorithm for finding a minimal spanning tree by adding edges in order of increasing weight if they do not form cycles.
Recommended
Vanmathy no sql
Element of graph four types vertex edge path loop operation of graph three type union of graph intersection of graph graph traversal
VANU no sql ppt.pptx
The document discusses elements and operations related to graphs. It defines key graph elements like vertices, edges, loops, and degrees of vertices. It also describes operations on graphs such as finding paths and circuits, determining connectivity, and extracting subgraphs. Various graph types and conversions between directed and undirected graphs are also covered.
DATA STRUCTURE PRESENTATION.pptx
This presentation summarizes key concepts about graphs. It defines a graph as a pair of sets (V,E) where V is the set of vertices and E is the set of edges. It discusses types of graphs like simple graphs and connected graphs. It also defines important graph concepts such as subgraphs, walks, Euler paths and circuits, and shortest path problems. The presentation was delivered to lecturers in the Computer Science department on the topic of graphs.
Graphs
A basic tutorial on the elementary graph theory and its implementations using data structures.
This tutorial deals with implementation of graphs in programs using data structures ,traversal algorithms: BFS, DFS, minimal spanning trees, Kruskal's algorithm, Prim's algorithm, Shortest path problem: Dijkastra's algorithm with graphical features.
DIGITAL TEXT BOOK
The document discusses various distance metrics that can be defined on the vertices of graphs. It defines shortest path distance (also called geodesic distance) as the length of the shortest path between two vertices, which satisfies the properties of a metric. Minimum weighted path distance is defined similarly for weighted graphs. The graph diameter is defined as the maximum shortest path distance between any two vertices of a connected graph. It provides examples to illustrate these distance concepts on graphs.
Magtibay buk bind#2
The document discusses Hamiltonian graphs, which are graphs that contain a Hamiltonian circuit or path. A Hamiltonian circuit visits each vertex in the graph exactly once and forms a cycle. The document provides an example of a graph that is Hamiltonian but not Eulerian, and vice versa. It notes that while it is clear only connected graphs can be Hamiltonian, there is no simple criterion to determine if a graph is Hamiltonian like there is for Eulerian graphs. It presents Dirac's sufficient condition for a graph to be Hamiltonian.
A glimpse to topological graph theory
This document provides an introduction to topological graph theory. It begins with definitions of basic graph theory concepts from a topological perspective, such as representing graphs with curved arcs instead of straight lines. It then discusses graph drawings, incidence matrices, vertex valence, and graph maps/isomorphisms. Important classes of graphs are introduced, such as trees, paths, cycles, and complete graphs. The document aims to introduce preliminary concepts of topological graph theory to students in a simple manner.
Graph applications chapter
This document summarizes algorithms for finding connected components, topological sorting of directed acyclic graphs (DAGs), and finding minimal spanning trees in weighted undirected graphs. It describes:
1) Using breadth-first or depth-first search to find the connected components of an undirected graph by traversing from each unvisited vertex.
2) Topological sorting of DAGs by recursively traversing vertices in depth-first order and listing them in the order they are finished.
3) Kruskal's algorithm for finding a minimal spanning tree by adding edges in order of increasing weight if they do not form cycles.
FCS (graphs).pptx
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.
20131216 Stat Journal
This document describes a new algorithm called GRAph ALigner (GRAAL) for topological network alignment. GRAAL aims to provide a unique global alignment of nodes between two networks based solely on topological similarity, without using other a priori information. It works by first finding a dense core between the networks to seed the alignment, then expanding outwards in spheres of increasing radius to align additional nodes. The alignment score is based on the percentage of edges from the first network that are correctly aligned to edges in the second network. The algorithm is tested on sample networks and achieves an edge correctness of 0.089.
Graph theory
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.
Graph theory concepts complex networks presents-rouhollah nabati
This document provides an introduction to network and social network analysis theory, including basic concepts of graph theory and network structures. It defines what a network and graph are, explains what network theory techniques are used for, and gives examples of real-world networks that can be represented as graphs. It also summarizes key graph theory concepts such as nodes, edges, walks, paths, cycles, connectedness, degree, and centrality measures.
ON ALGORITHMIC PROBLEMS CONCERNING GRAPHS OF HIGHER DEGREE OF SYMMETRY
Since the ancient determination of the five platonic solids the study of symmetry and regularity has always
been one of the most fascinating aspects of mathematics. One intriguing phenomenon of studies in graph
theory is the fact that quite often arithmetic regularity properties of a graph imply the existence of many
symmetries, i.e. large automorphism group G. In some important special situation higher degree of
regularity means that G is an automorphism group of finite geometry. For example, a glance through the
list of distance regular graphs of diameter d < 3 reveals the fact that most of them are connected with
classical Lie geometry. Theory of distance regular graphs is an important part of algebraic combinatorics
and its applications such as coding theory, communication networks, and block design. An important tool
for investigation of such graphs is their spectra, which is the set of eigenvalues of adjacency matrix of a
graph. Let G be a finite simple group of Lie type and X be the set homogeneous elements of the associated
geometry.
Graph (Data structure)
This document discusses three types of graphs: directed graphs, undirected graphs, and weighted graphs. It provides examples and definitions of basic graph terminology like vertices, edges, and paths. It also describes two common ways to represent graphs in computer memory: sequential representation using adjacency lists and linked representation using linked lists. Finally, it outlines high-level processes for creating a graph and searching or deleting elements from a graph.
Operations on graph
This PowerPoint contains introduction of basic operations like subgraph, union of graph , complement of graph
Graphs
This document defines and explains key concepts related to graphs. It defines a graph as G=(V,E) where V is a set of vertices and E is a set of edges. It distinguishes between directed and undirected graphs. Key graph terminology explained includes adjacent nodes, paths, cycles, degrees, and connections. Graph searching algorithms depth-first search (DFS) and breadth-first search (BFS) are also summarized, including their ideas and implementations.
Tn 110 lecture 8
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.
On algorithmic problems concerning graphs of higher degree of symmetry
Since the ancient determination of the five platonic solids the study of symmetry and regularity has always
been one of the most fascinating aspects of mathematics. One intriguing phenomenon of studies in graph
theory is the fact that quite often arithmetic regularity properties of a graph imply the existence of many
symmetries, i.e. large automorphism group G. In some important special situation higher degree of
regularity means that G is an automorphism group of finite geometry. For example, a glance through the
list of distance regular graphs of diameter d < 3 reveals the fact that most of them are connected with
classical Lie geometry. Theory of distance regular graphs is an important part of algebraic combinatorics
and its applications such as coding theory, communication networks, and block design. An important tool
for investigation of such graphs is their spectra, which is the set of eigenvalues of adjacency matrix of a
graph. Let G be a finite simple group of Lie type and X be the set homogeneous elements of the associated
geometry. The complexity of computing the adjacency matrices of a graph Gr on the vertices X such that
Aut GR = G depends very much on the description of the geometry with which one starts. For example, we
can represent the geometry as the totality of 1 cosets of parabolic subgroups 2 chains of embedded
subspaces (case of linear groups), or totally isotropic subspaces (case of the remaining classical groups), 3
special subspaces of minimal module for G which are defined in terms of a G invariant multilinear form.
The aim of this research is to develop an effective method for generation of graphs connected with classical
geometry and evaluation of its spectra, which is the set of eigenvalues of adjacency matrix of a graph. The
main approach is to avoid manual drawing and to calculate graph layout automatically according to its
formal structure. This is a simple task in a case of a tree like graph with a strict hierarchy of entities but it
becomes more complicated for graphs of geometrical nature. There are two main reasons for the
investigations of spectra: (1) very often spectra carry much more useful information about the graph than a
corresponding list of entities and relationships (2) graphs with special spectra, satisfying so called
Ramanujan property or simply Ramanujan graphs (by name of Indian genius mathematician) are important
for real life applications (see [13]). There is a motivated suspicion that among geometrical graphs one
could find some new Ramanujan graphs.
Data structure graphs
Graphs are non-linear data structures that can be used to represent relationships between objects. A graph contains vertices (nodes) connected by edges (links). A graph G is defined as a set of vertices V connected by a set of edges E. For example, a graph G can be defined as G = (V, E) where V = {A,B,C,D,E} and E = {(A,B), (A,C), (A,D), (B,D), (C,D), (B,E), (E,D)}. Graphs can model real-world networks like roads connecting cities. Euler used graphs to solve the Königsberg bridge problem by showing
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
The document discusses graph isomorphism, which is determining if two graphs can be drawn in the same way. Two graphs are isomorphic if there is a one-to-one correspondence between their vertices that preserves adjacency. The document also provides examples of isomorphic and non-isomorphic graphs. It further discusses concepts like paths, connectedness, subgraphs, cut-sets, Euler paths and circuits, and Hamilton paths and circuits. Theorems related to conditions for the existence of Eulerian and Hamiltonian graphs are also presented.
Chapter 1
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.
BCA_Semester-II-Discrete Mathematics_unit-iv Graph theory
This document defines key concepts in graph theory, including:
- A graph is defined as a pair (V,E) where V is the set of vertices and E is the set of edges.
- Examples of graph terminology include vertices, edges, walks, paths, circuits, connectivity, and components.
- Different types of graphs are discussed such as simple graphs, complete graphs, subgraphs, and induced subgraphs.
graph.ppt
Graph theory concepts can be applied in various domains such as computer networks, chemistry, and transportation. Key graph theory concepts include:
- Graphs are represented by vertices (nodes) and edges, and can be directed or undirected. Common graph types include trees, cycles, and bipartite graphs.
- Graphs can be represented through matrices like the incidence matrix and adjacency matrix which describe the relationships between vertices and edges. Adjacency lists are another representation.
- Connectivity describes the reachability between vertices via paths along edges. A graph is connected if there is a path between all pairs of vertices.
- Other concepts include isomorphism, which determines if two graphs have the same structure, and
Graph theory
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.
DATA STRUCTURES.pptx
The document discusses graphs and graph algorithms. It begins by defining what a graph is - a collection of vertices connected by edges. It then lists four learning objectives related to representing graphs, traversing graphs, calculating minimum spanning trees, and finding shortest routes. The document goes on to describe different ways of representing graphs through adjacency matrices and lists. It also explains graph traversal algorithms like depth-first search and breadth-first search. Finally, it discusses algorithms for finding minimum spanning trees and shortest paths in weighted graphs.
logic.pptx
The document discusses graphs and graph algorithms. It defines what a graph is and how they can be represented. It also explains graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). Additionally, it covers algorithms for finding the shortest path using Dijkstra's algorithm and calculating minimum spanning trees using Kruskal's algorithm.
NON-LINEAR DATA STRUCTURE-Graphs.pptx
The document defines graphs and discusses their properties and applications. It covers topics like directed vs undirected graphs, representations using adjacency matrices and lists, graph traversals using depth-first and breadth-first search, minimum spanning trees, and applications of graphs in areas like social networks and the world wide web.
Graphs and eularian circuit & path with c++ program
This document discusses graphs and Eulerian paths and circuits. It begins by defining what a graph is - a set of nodes and edges. It then describes different types of graphs like directed/undirected, cyclic/acyclic, labeled, and weighted graphs. It explains the concepts of adjacency and connectivity in graphs. The document focuses on Eulerian paths and circuits, providing properties for a graph to have an Eulerian path or circuit. It presents pseudocode for an algorithm to check if a graph is Eulerian using depth-first search. Finally, it includes C++ code for a program that tests if input graphs exhibit an Eulerian path or circuit.
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
How to Download & Install Module From the Odoo App Store in Odoo 17
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
More Related Content
Similar to Table of Contents-.pptx
FCS (graphs).pptx
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.
20131216 Stat Journal
This document describes a new algorithm called GRAph ALigner (GRAAL) for topological network alignment. GRAAL aims to provide a unique global alignment of nodes between two networks based solely on topological similarity, without using other a priori information. It works by first finding a dense core between the networks to seed the alignment, then expanding outwards in spheres of increasing radius to align additional nodes. The alignment score is based on the percentage of edges from the first network that are correctly aligned to edges in the second network. The algorithm is tested on sample networks and achieves an edge correctness of 0.089.
Graph theory
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.
Graph theory concepts complex networks presents-rouhollah nabati
This document provides an introduction to network and social network analysis theory, including basic concepts of graph theory and network structures. It defines what a network and graph are, explains what network theory techniques are used for, and gives examples of real-world networks that can be represented as graphs. It also summarizes key graph theory concepts such as nodes, edges, walks, paths, cycles, connectedness, degree, and centrality measures.
ON ALGORITHMIC PROBLEMS CONCERNING GRAPHS OF HIGHER DEGREE OF SYMMETRY
Since the ancient determination of the five platonic solids the study of symmetry and regularity has always
been one of the most fascinating aspects of mathematics. One intriguing phenomenon of studies in graph
theory is the fact that quite often arithmetic regularity properties of a graph imply the existence of many
symmetries, i.e. large automorphism group G. In some important special situation higher degree of
regularity means that G is an automorphism group of finite geometry. For example, a glance through the
list of distance regular graphs of diameter d < 3 reveals the fact that most of them are connected with
classical Lie geometry. Theory of distance regular graphs is an important part of algebraic combinatorics
and its applications such as coding theory, communication networks, and block design. An important tool
for investigation of such graphs is their spectra, which is the set of eigenvalues of adjacency matrix of a
graph. Let G be a finite simple group of Lie type and X be the set homogeneous elements of the associated
geometry.
Graph (Data structure)
This document discusses three types of graphs: directed graphs, undirected graphs, and weighted graphs. It provides examples and definitions of basic graph terminology like vertices, edges, and paths. It also describes two common ways to represent graphs in computer memory: sequential representation using adjacency lists and linked representation using linked lists. Finally, it outlines high-level processes for creating a graph and searching or deleting elements from a graph.
Operations on graph
This PowerPoint contains introduction of basic operations like subgraph, union of graph , complement of graph
Graphs
This document defines and explains key concepts related to graphs. It defines a graph as G=(V,E) where V is a set of vertices and E is a set of edges. It distinguishes between directed and undirected graphs. Key graph terminology explained includes adjacent nodes, paths, cycles, degrees, and connections. Graph searching algorithms depth-first search (DFS) and breadth-first search (BFS) are also summarized, including their ideas and implementations.
Tn 110 lecture 8
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.
On algorithmic problems concerning graphs of higher degree of symmetry
Since the ancient determination of the five platonic solids the study of symmetry and regularity has always
been one of the most fascinating aspects of mathematics. One intriguing phenomenon of studies in graph
theory is the fact that quite often arithmetic regularity properties of a graph imply the existence of many
symmetries, i.e. large automorphism group G. In some important special situation higher degree of
regularity means that G is an automorphism group of finite geometry. For example, a glance through the
list of distance regular graphs of diameter d < 3 reveals the fact that most of them are connected with
classical Lie geometry. Theory of distance regular graphs is an important part of algebraic combinatorics
and its applications such as coding theory, communication networks, and block design. An important tool
for investigation of such graphs is their spectra, which is the set of eigenvalues of adjacency matrix of a
graph. Let G be a finite simple group of Lie type and X be the set homogeneous elements of the associated
geometry. The complexity of computing the adjacency matrices of a graph Gr on the vertices X such that
Aut GR = G depends very much on the description of the geometry with which one starts. For example, we
can represent the geometry as the totality of 1 cosets of parabolic subgroups 2 chains of embedded
subspaces (case of linear groups), or totally isotropic subspaces (case of the remaining classical groups), 3
special subspaces of minimal module for G which are defined in terms of a G invariant multilinear form.
The aim of this research is to develop an effective method for generation of graphs connected with classical
geometry and evaluation of its spectra, which is the set of eigenvalues of adjacency matrix of a graph. The
main approach is to avoid manual drawing and to calculate graph layout automatically according to its
formal structure. This is a simple task in a case of a tree like graph with a strict hierarchy of entities but it
becomes more complicated for graphs of geometrical nature. There are two main reasons for the
investigations of spectra: (1) very often spectra carry much more useful information about the graph than a
corresponding list of entities and relationships (2) graphs with special spectra, satisfying so called
Ramanujan property or simply Ramanujan graphs (by name of Indian genius mathematician) are important
for real life applications (see [13]). There is a motivated suspicion that among geometrical graphs one
could find some new Ramanujan graphs.
Data structure graphs
Graphs are non-linear data structures that can be used to represent relationships between objects. A graph contains vertices (nodes) connected by edges (links). A graph G is defined as a set of vertices V connected by a set of edges E. For example, a graph G can be defined as G = (V, E) where V = {A,B,C,D,E} and E = {(A,B), (A,C), (A,D), (B,D), (C,D), (B,E), (E,D)}. Graphs can model real-world networks like roads connecting cities. Euler used graphs to solve the Königsberg bridge problem by showing
ISOMORFISME, CONNECTIVITY EULER HAMILTON.pdf
The document discusses graph isomorphism, which is determining if two graphs can be drawn in the same way. Two graphs are isomorphic if there is a one-to-one correspondence between their vertices that preserves adjacency. The document also provides examples of isomorphic and non-isomorphic graphs. It further discusses concepts like paths, connectedness, subgraphs, cut-sets, Euler paths and circuits, and Hamilton paths and circuits. Theorems related to conditions for the existence of Eulerian and Hamiltonian graphs are also presented.
Chapter 1
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.
BCA_Semester-II-Discrete Mathematics_unit-iv Graph theory
This document defines key concepts in graph theory, including:
- A graph is defined as a pair (V,E) where V is the set of vertices and E is the set of edges.
- Examples of graph terminology include vertices, edges, walks, paths, circuits, connectivity, and components.
- Different types of graphs are discussed such as simple graphs, complete graphs, subgraphs, and induced subgraphs.
graph.ppt
Graph theory concepts can be applied in various domains such as computer networks, chemistry, and transportation. Key graph theory concepts include:
- Graphs are represented by vertices (nodes) and edges, and can be directed or undirected. Common graph types include trees, cycles, and bipartite graphs.
- Graphs can be represented through matrices like the incidence matrix and adjacency matrix which describe the relationships between vertices and edges. Adjacency lists are another representation.
- Connectivity describes the reachability between vertices via paths along edges. A graph is connected if there is a path between all pairs of vertices.
- Other concepts include isomorphism, which determines if two graphs have the same structure, and
Graph theory
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.
DATA STRUCTURES.pptx
The document discusses graphs and graph algorithms. It begins by defining what a graph is - a collection of vertices connected by edges. It then lists four learning objectives related to representing graphs, traversing graphs, calculating minimum spanning trees, and finding shortest routes. The document goes on to describe different ways of representing graphs through adjacency matrices and lists. It also explains graph traversal algorithms like depth-first search and breadth-first search. Finally, it discusses algorithms for finding minimum spanning trees and shortest paths in weighted graphs.
logic.pptx
The document discusses graphs and graph algorithms. It defines what a graph is and how they can be represented. It also explains graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). Additionally, it covers algorithms for finding the shortest path using Dijkstra's algorithm and calculating minimum spanning trees using Kruskal's algorithm.
NON-LINEAR DATA STRUCTURE-Graphs.pptx
The document defines graphs and discusses their properties and applications. It covers topics like directed vs undirected graphs, representations using adjacency matrices and lists, graph traversals using depth-first and breadth-first search, minimum spanning trees, and applications of graphs in areas like social networks and the world wide web.
Graphs and eularian circuit & path with c++ program
This document discusses graphs and Eulerian paths and circuits. It begins by defining what a graph is - a set of nodes and edges. It then describes different types of graphs like directed/undirected, cyclic/acyclic, labeled, and weighted graphs. It explains the concepts of adjacency and connectivity in graphs. The document focuses on Eulerian paths and circuits, providing properties for a graph to have an Eulerian path or circuit. It presents pseudocode for an algorithm to check if a graph is Eulerian using depth-first search. Finally, it includes C++ code for a program that tests if input graphs exhibit an Eulerian path or circuit.
Similar to Table of Contents-.pptx (20)
Graph theory concepts complex networks presents-rouhollah nabati
Graph theory concepts complex networks presents-rouhollah nabati
ON ALGORITHMIC PROBLEMS CONCERNING GRAPHS OF HIGHER DEGREE OF SYMMETRY
ON ALGORITHMIC PROBLEMS CONCERNING GRAPHS OF HIGHER DEGREE OF SYMMETRY
On algorithmic problems concerning graphs of higher degree of symmetry
On algorithmic problems concerning graphs of higher degree of symmetry
BCA_Semester-II-Discrete Mathematics_unit-iv Graph theory
BCA_Semester-II-Discrete Mathematics_unit-iv Graph theory
Graphs and eularian circuit & path with c++ program
Graphs and eularian circuit & path with c++ program
Recently uploaded
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
How to Download & Install Module From the Odoo App Store in Odoo 17
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
Contiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptx
HYPERTENSION - SLIDE SHARE PRESENTATION.
IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
220711130082 Srabanti Bag Internet Resources For Natural Science
Internet resources for natural science
Educational Technology in the Health Sciences
Plenary presentation at the NTTC Inter-university Workshop, 18 June 2024, Manila Prince Hotel.
Brand Guideline of Bashundhara A4 Paper - 2024
It outlines the basic identity elements such as symbol, logotype, colors, and typefaces. It provides examples of applying the identity to materials like letterhead, business cards, reports, folders, and websites.
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
Aims and objectives of national policy on information and communication technology(ICT) in school education in india
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...Nguyen Thanh Tu Collection
https://app.box.com/s/nrwz52lilmrw6m5kqeqn83q6vbdp8yzpCreation or Update of a Mandatory Field is Not Set in Odoo 17
In this slide we will discuss Creation or Updation of a mandatory field is not set in Odoo 17.
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...Nguyen Thanh Tu Collection
https://app.box.com/s/qspvswamcohjtbvbbhjad04lg65waylfTHE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
Recently uploaded (20)
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
Contiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptx
220711130082 Srabanti Bag Internet Resources For Natural Science
220711130082 Srabanti Bag Internet Resources For Natural Science
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
220711130088 Sumi Basak Virtual University EPC 3.pptx
220711130088 Sumi Basak Virtual University EPC 3.pptx
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
Creation or Update of a Mandatory Field is Not Set in Odoo 17
Creation or Update of a Mandatory Field is Not Set in Odoo 17
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
Table of Contents-.pptx
- 2. Table of Contents:- INTRODUCTION ISOMORPHISM SUB GRAPHS WALKS PATHS
- 3. Introduction Agraph is determined as a mathematical structure that represents a particular function by connecting a set of points.
- 4. Isomorphism IF WE ARE GIVEN TWO SIMPLE GRAPHS, G AND H. GRAPHS G AND H ARE ISOMORPHIC IF THERE IS A STRUCTURE THAT PRESERVES A ONE-TO- ONE CORRESPONDENCE BETWEEN THE VERTICES AND EDGES.
- 5. Sub Graphs A GRAPH G1 = (V1, E1) IS CALLED A SUBGRAPH OF A GRAPH G(V, E) IF V1(G) IS A SUBSET OF V(G) AND E1(G) IS A SUBSET OF E(G) SUCH THAT EACH EDGE OF G1 HAS SAME END VERTICES AS IN G.
- 6. A walk can be defined as a sequence of edgesandvertices of a graph. Walks
- 7. Paths APATHIS ASEQUENCE OFEDGES THAT BEGINS A TAVERTEX, AND TRAVELS FROM VERTEXTOVERTEXALONG EDGES OFTHE GRAPH.