Graph labeling is a remarkable field having direct and indirect involvement in resolving numerous issues in varied fields. During this paper we tend to planned new algorithms to construct edge antimagic vertex labeling, edge antimagic total labeling, (a, d)-edge antimagic vertex labeling, (a, d)-edge antimagic total labeling and super edge antimagic labeling of varied classes of graphs like paths, cycles, wheels, fans, friendship graphs. With these solutions several open issues during this space can be solved.
Cordial Labelings in the Context of TriplicationIRJET Journal
This document presents research on graph labelings for the extended triplicate graph of a ladder graph. It begins with an introduction to graph theory concepts like graph labelings and defines cordial, total cordial, product cordial, and total product cordial labelings. It then provides an algorithm to construct the extended triplicate graph of a ladder graph and proves that this graph admits cordial, total cordial, product cordial, and total product cordial labelings. Algorithms are presented for each type of labeling and proofs are given that the number of vertices and edges labeled 0 and 1 differ by at most 1, satisfying the conditions for these labeling types.
1. The document introduces hypergraphs as an extension of graphs where edges can connect more than two vertices.
2. Hypergraphs are useful for applications like image and video segmentation where they can retain more information compared to simple graphs.
3. The document provides examples of using hypergraphs for tasks like video object segmentation, multiple target tracking, multi-view reconstruction, and matching in computer vision.
The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric G X × X × X ® R+ d : where X = r(v /W) =
{(d(v,v1),d(v,v2 ),...,d(v,v ) / v V (G))} k Î , denoted d G and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if d G
numbers of pendant edges are added to the non-basis vertices.
METRIC DIMENSION AND UNCERTAINTY OF TRAVERSING ROBOTS IN A NETWORKgraphhoc
Metric dimension in graph theory has many applications in the real world. It has been applied to the
optimization problems in complex networks, analyzing electrical networks; show the business relations,
robotics, control of production processes etc. This paper studies the metric dimension of graphs with
respect to contraction and its bijection between them. Also an algorithm to avoid the overlapping between
the robots in a network is introduced.
The document is a research paper that presents new results on odd harmonious graphs. It introduces the concepts of m-shadow graphs and m-splitting graphs. The paper proves that m-shadow graphs of paths and complete bipartite graphs are odd harmonious for all m ≥ 1. It also proves that n-splitting graphs of paths, stars and symmetric products of paths and null graphs are odd harmonious for all n ≥ 1. Additional families of graphs, including m-shadow graphs of stars and various graph constructions using paths, stars and their splitting graphs, are shown to admit odd harmonious labeling.
A Study on Power Mean Labeling of the Graphs and Vertex Odd Power Mean Labeli...ijtsrd
This paper we discuss with power mean labeling of graph and Vertex Odd Power Mean Labeling of Graphs. A graph = , is referred as Power Mean graph with , q , if it is feasible to label the vertices with different elements from 1, 2, 3, ..., 1 in such a way that when each edge = is labeled with f e=uv = f u f v f v f u 1 f u f v In this paper we define Vertex Odd Power Mean labeling and investigate the same for some graphs. We define Vertex Odd Power Mean labeling for the graph G V, E with vertices and q edges, if it is feasible to label the vertices with different labelings f from {1, 3, 5, ..., 2 – 1} in such a way that when each edge = is labeled with f e=uv = f u f v f v f u 1 f u f v or f e=uv = f u f v f v f u 1 f u f v and the edge labeling are distinct. The graph which admits the Vertex Odd Power Mean labeling, is called Vertex Odd Power Mean graph. B. Kavitha | Dr. C. Vimala "A Study on Power Mean Labeling of the Graphs and Vertex Odd Power Mean Labeling of Graphs" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38116.pdf Paper URL : https://www.ijtsrd.com/mathemetics/applied-mathematics/38116/a-study-on-power-mean-labeling-of-the-graphs-and-vertex-odd-power-mean-labeling-of-graphs/b-kavitha
A study on connectivity in graph theory june 18 pdfaswathymaths
This document provides an introduction and two chapters on connectivity in graphs. The introduction discusses the history and applications of graph theory. Chapter 1 defines key concepts related to connectivity such as bridges, cut vertices, and k-connectivity. It presents theorems characterizing when an edge is a bridge and when a graph is a tree. Chapter 2 discusses applications of connectivity in graphs.
Connected domination in block subdivision graphs of graphsAlexander Decker
This document discusses connected domination in block subdivision graphs. It begins by defining key terms such as domination, connected domination, block subdivision graphs, and connected domination number. It then presents three theorems that establish bounds on the connected domination number of block subdivision graphs in terms of the number of vertices and cut vertices of the original graph G.
Cordial Labelings in the Context of TriplicationIRJET Journal
This document presents research on graph labelings for the extended triplicate graph of a ladder graph. It begins with an introduction to graph theory concepts like graph labelings and defines cordial, total cordial, product cordial, and total product cordial labelings. It then provides an algorithm to construct the extended triplicate graph of a ladder graph and proves that this graph admits cordial, total cordial, product cordial, and total product cordial labelings. Algorithms are presented for each type of labeling and proofs are given that the number of vertices and edges labeled 0 and 1 differ by at most 1, satisfying the conditions for these labeling types.
1. The document introduces hypergraphs as an extension of graphs where edges can connect more than two vertices.
2. Hypergraphs are useful for applications like image and video segmentation where they can retain more information compared to simple graphs.
3. The document provides examples of using hypergraphs for tasks like video object segmentation, multiple target tracking, multi-view reconstruction, and matching in computer vision.
The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric G X × X × X ® R+ d : where X = r(v /W) =
{(d(v,v1),d(v,v2 ),...,d(v,v ) / v V (G))} k Î , denoted d G and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if d G
numbers of pendant edges are added to the non-basis vertices.
METRIC DIMENSION AND UNCERTAINTY OF TRAVERSING ROBOTS IN A NETWORKgraphhoc
Metric dimension in graph theory has many applications in the real world. It has been applied to the
optimization problems in complex networks, analyzing electrical networks; show the business relations,
robotics, control of production processes etc. This paper studies the metric dimension of graphs with
respect to contraction and its bijection between them. Also an algorithm to avoid the overlapping between
the robots in a network is introduced.
The document is a research paper that presents new results on odd harmonious graphs. It introduces the concepts of m-shadow graphs and m-splitting graphs. The paper proves that m-shadow graphs of paths and complete bipartite graphs are odd harmonious for all m ≥ 1. It also proves that n-splitting graphs of paths, stars and symmetric products of paths and null graphs are odd harmonious for all n ≥ 1. Additional families of graphs, including m-shadow graphs of stars and various graph constructions using paths, stars and their splitting graphs, are shown to admit odd harmonious labeling.
A Study on Power Mean Labeling of the Graphs and Vertex Odd Power Mean Labeli...ijtsrd
This paper we discuss with power mean labeling of graph and Vertex Odd Power Mean Labeling of Graphs. A graph = , is referred as Power Mean graph with , q , if it is feasible to label the vertices with different elements from 1, 2, 3, ..., 1 in such a way that when each edge = is labeled with f e=uv = f u f v f v f u 1 f u f v In this paper we define Vertex Odd Power Mean labeling and investigate the same for some graphs. We define Vertex Odd Power Mean labeling for the graph G V, E with vertices and q edges, if it is feasible to label the vertices with different labelings f from {1, 3, 5, ..., 2 – 1} in such a way that when each edge = is labeled with f e=uv = f u f v f v f u 1 f u f v or f e=uv = f u f v f v f u 1 f u f v and the edge labeling are distinct. The graph which admits the Vertex Odd Power Mean labeling, is called Vertex Odd Power Mean graph. B. Kavitha | Dr. C. Vimala "A Study on Power Mean Labeling of the Graphs and Vertex Odd Power Mean Labeling of Graphs" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38116.pdf Paper URL : https://www.ijtsrd.com/mathemetics/applied-mathematics/38116/a-study-on-power-mean-labeling-of-the-graphs-and-vertex-odd-power-mean-labeling-of-graphs/b-kavitha
A study on connectivity in graph theory june 18 pdfaswathymaths
This document provides an introduction and two chapters on connectivity in graphs. The introduction discusses the history and applications of graph theory. Chapter 1 defines key concepts related to connectivity such as bridges, cut vertices, and k-connectivity. It presents theorems characterizing when an edge is a bridge and when a graph is a tree. Chapter 2 discusses applications of connectivity in graphs.
Connected domination in block subdivision graphs of graphsAlexander Decker
This document discusses connected domination in block subdivision graphs. It begins by defining key terms such as domination, connected domination, block subdivision graphs, and connected domination number. It then presents three theorems that establish bounds on the connected domination number of block subdivision graphs in terms of the number of vertices and cut vertices of the original graph G.
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.
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
The document discusses connectivity in graphs. It defines edge connectivity and vertex connectivity as numerical parameters that measure how connected a graph is. Edge connectivity is the minimum number of edges that need to be removed to disconnect the graph. Vertex connectivity is defined similarly for vertices. It provides examples and discusses properties like cut sets, bridges, and the relationship between these concepts and connectivity values. Menger's theorem relating the size of the minimum cut to the maximum number of disjoint paths is also covered.
IRJET- Independent Middle Domination Number in Jump GraphIRJET Journal
This document discusses independent middle domination number (iM(J(G))) in jump graphs. It defines iM(J(G)) as the minimum cardinality of an independent dominating set of the middle graph M(J(G)). The paper obtains several bounds on iM(J(G)) in terms of the vertices, edges, and other parameters of J(G). It also establishes relationships between iM(J(G)) and other domination parameters such as domination number, strong split domination number, and edge domination number. Exact values of iM(J(G)) are determined for some standard jump graphs like paths, cycles, stars, and wheels.
This document defines key graph terminology and concepts. It begins by defining what a graph is composed of - vertices and edges. It then discusses directed vs undirected graphs and defines common graph terms like adjacent vertices, paths, cycles, and more. The document also covers different ways to represent graphs, such as adjacency matrices and adjacency lists. Finally, it briefly introduces common graph search methods like breadth-first search and depth-first search.
E-Cordial Labeling of Some Mirror GraphsWaqas Tariq
Let G be a bipartite graph with a partite sets V1 and V2 and G\' be the copy of G with corresponding partite sets V1\' and V2\' . The mirror graph M(G) of G is obtained from G and G\' by joining each vertex of V2 to its corresponding vertex in V2\' by an edge. Here we investigate E-cordial labeling of some mirror graphs. We prove that the mirror graphs of even cycle Cn, even path Pn and hypercube Qk are E-cordial graphs.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Strong (Weak) Triple Connected Domination Number of a Fuzzy Graphijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
EVEN GRACEFUL LABELLING OF A CLASS OF TREESFransiskeran
A labelling or numbering of a graph G with q edges is an assignment of labels to the vertices of G that
induces for each edge uv a labelling depending on the vertex labels f(u) and f(v). A labelling is called a
graceful labelling if there exists an injective function f: V (G) → {0, 1,2,......q} such that for each edge xy,
the labelling │f(x)-f(y)│is distinct. In this paper, we prove that a class of Tn trees are even graceful.
The document describes how snakes, or active contours, can be used to model shapes in images. It discusses how snakes work by defining an energy function along a curve and minimizing that energy to find the optimal curve. The energy includes an internal term based on curvature and an external term from image features. Level sets are used to propagate the curves towards the minimum energy configuration using gradient descent. Key steps include modeling the shape as a curve, defining the energy function, deriving the curve to minimize energy via calculus of variations, and propagating the curves using level sets.
The document discusses claw decompositions of product graphs. It provides necessary and sufficient conditions for decomposing the Cartesian product of standard graphs into claws. Some key results are:
1. If G1 and G2 are claw decomposable, then their Cartesian product G1 x G2 is also claw decomposable.
2. The Cartesian product of complete graphs or complete bipartite graphs is claw decomposable if certain conditions on their vertex sets are met.
3. Sufficient conditions are given for the lexicographic product of a graph G with Km, Kn, or K2 x Kn to be claw decomposable when m and n satisfy certain properties.
So in summary, the document
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a ’heteromorphism’ which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations of quantum groups and the Yang-Baxter equation are presented.
IRJET- On Distributive Meet-SemilatticesIRJET Journal
This document discusses various notions of distributivity for meet-semilattices that generalize the usual notion of distributivity in lattices. It defines six notions of distributivity - GS-distributivity, K-distributivity, H-distributivity, LR-distributivity, B-distributivity, and -distributivity. It proves that these notions are linearly ordered from weakest to strongest as GS, K, H=LR, B, -distributivity. It provides counterexamples to show the implications do not go in the reverse direction and that the notions are non-equivalent generalizations of distributivity for lattices to meet-semilattices
This document proposes a novel image encryption technique based on multiple fuzzy graph mappings. It begins by introducing fuzzy graphs and fuzzy membership functions. It then describes how to generate multiple fuzzy graphs from a single matrix using different membership functions and parameter values. These fuzzy graphs are then mapped onto an image to encrypt it. The encryption process has three main steps: 1) pixel shuffling, 2) fuzzy graph mappings, and 3) image encryption based on the multiple fuzzy graph mappings. Experimental results demonstrate that the proposed technique is efficient and provides robust encryption.
Zaharescu__Eugen Color Image Indexing Using Mathematical MorphologyEugen Zaharescu
This document discusses using mathematical morphology techniques for color image indexing. It proposes using morphological signatures as powerful descriptions of image content. Morphological signatures are defined as a series of morphological operations (openings and closings) using structuring elements of varying sizes. For color images, morphological feature extraction algorithms are used that include more complex operators like color gradient, homotopic skeleton, and Hit-or-Miss transform. Examples applying this approach on real images are also provided.
A study on connectivity in graph theory june 18 123easwathymaths
This document provides an introduction to connectivity of graphs. It begins with definitions of terms like bridges, cut vertices, connectivity, and edge connectivity. It then presents several theorems about when edges are bridges and vertices are cut vertices. It proves properties of trees related to cut vertices. The document establishes relationships between vertex and edge connectivity. It introduces the concepts of k-connectivity and discusses properties of complete graphs and trees in relation to connectivity.
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.
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
The document discusses connectivity in graphs. It defines edge connectivity and vertex connectivity as numerical parameters that measure how connected a graph is. Edge connectivity is the minimum number of edges that need to be removed to disconnect the graph. Vertex connectivity is defined similarly for vertices. It provides examples and discusses properties like cut sets, bridges, and the relationship between these concepts and connectivity values. Menger's theorem relating the size of the minimum cut to the maximum number of disjoint paths is also covered.
IRJET- Independent Middle Domination Number in Jump GraphIRJET Journal
This document discusses independent middle domination number (iM(J(G))) in jump graphs. It defines iM(J(G)) as the minimum cardinality of an independent dominating set of the middle graph M(J(G)). The paper obtains several bounds on iM(J(G)) in terms of the vertices, edges, and other parameters of J(G). It also establishes relationships between iM(J(G)) and other domination parameters such as domination number, strong split domination number, and edge domination number. Exact values of iM(J(G)) are determined for some standard jump graphs like paths, cycles, stars, and wheels.
This document defines key graph terminology and concepts. It begins by defining what a graph is composed of - vertices and edges. It then discusses directed vs undirected graphs and defines common graph terms like adjacent vertices, paths, cycles, and more. The document also covers different ways to represent graphs, such as adjacency matrices and adjacency lists. Finally, it briefly introduces common graph search methods like breadth-first search and depth-first search.
E-Cordial Labeling of Some Mirror GraphsWaqas Tariq
Let G be a bipartite graph with a partite sets V1 and V2 and G\' be the copy of G with corresponding partite sets V1\' and V2\' . The mirror graph M(G) of G is obtained from G and G\' by joining each vertex of V2 to its corresponding vertex in V2\' by an edge. Here we investigate E-cordial labeling of some mirror graphs. We prove that the mirror graphs of even cycle Cn, even path Pn and hypercube Qk are E-cordial graphs.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Strong (Weak) Triple Connected Domination Number of a Fuzzy Graphijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
EVEN GRACEFUL LABELLING OF A CLASS OF TREESFransiskeran
A labelling or numbering of a graph G with q edges is an assignment of labels to the vertices of G that
induces for each edge uv a labelling depending on the vertex labels f(u) and f(v). A labelling is called a
graceful labelling if there exists an injective function f: V (G) → {0, 1,2,......q} such that for each edge xy,
the labelling │f(x)-f(y)│is distinct. In this paper, we prove that a class of Tn trees are even graceful.
The document describes how snakes, or active contours, can be used to model shapes in images. It discusses how snakes work by defining an energy function along a curve and minimizing that energy to find the optimal curve. The energy includes an internal term based on curvature and an external term from image features. Level sets are used to propagate the curves towards the minimum energy configuration using gradient descent. Key steps include modeling the shape as a curve, defining the energy function, deriving the curve to minimize energy via calculus of variations, and propagating the curves using level sets.
The document discusses claw decompositions of product graphs. It provides necessary and sufficient conditions for decomposing the Cartesian product of standard graphs into claws. Some key results are:
1. If G1 and G2 are claw decomposable, then their Cartesian product G1 x G2 is also claw decomposable.
2. The Cartesian product of complete graphs or complete bipartite graphs is claw decomposable if certain conditions on their vertex sets are met.
3. Sufficient conditions are given for the lexicographic product of a graph G with Km, Kn, or K2 x Kn to be claw decomposable when m and n satisfy certain properties.
So in summary, the document
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a ’heteromorphism’ which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations of quantum groups and the Yang-Baxter equation are presented.
IRJET- On Distributive Meet-SemilatticesIRJET Journal
This document discusses various notions of distributivity for meet-semilattices that generalize the usual notion of distributivity in lattices. It defines six notions of distributivity - GS-distributivity, K-distributivity, H-distributivity, LR-distributivity, B-distributivity, and -distributivity. It proves that these notions are linearly ordered from weakest to strongest as GS, K, H=LR, B, -distributivity. It provides counterexamples to show the implications do not go in the reverse direction and that the notions are non-equivalent generalizations of distributivity for lattices to meet-semilattices
This document proposes a novel image encryption technique based on multiple fuzzy graph mappings. It begins by introducing fuzzy graphs and fuzzy membership functions. It then describes how to generate multiple fuzzy graphs from a single matrix using different membership functions and parameter values. These fuzzy graphs are then mapped onto an image to encrypt it. The encryption process has three main steps: 1) pixel shuffling, 2) fuzzy graph mappings, and 3) image encryption based on the multiple fuzzy graph mappings. Experimental results demonstrate that the proposed technique is efficient and provides robust encryption.
Zaharescu__Eugen Color Image Indexing Using Mathematical MorphologyEugen Zaharescu
This document discusses using mathematical morphology techniques for color image indexing. It proposes using morphological signatures as powerful descriptions of image content. Morphological signatures are defined as a series of morphological operations (openings and closings) using structuring elements of varying sizes. For color images, morphological feature extraction algorithms are used that include more complex operators like color gradient, homotopic skeleton, and Hit-or-Miss transform. Examples applying this approach on real images are also provided.
A study on connectivity in graph theory june 18 123easwathymaths
This document provides an introduction to connectivity of graphs. It begins with definitions of terms like bridges, cut vertices, connectivity, and edge connectivity. It then presents several theorems about when edges are bridges and vertices are cut vertices. It proves properties of trees related to cut vertices. The document establishes relationships between vertex and edge connectivity. It introduces the concepts of k-connectivity and discusses properties of complete graphs and trees in relation to connectivity.
Iedereen is wel eens bang. En dat is maar goed ook, want zonder angst zou je als mens niet kunnen functioneren. Het waarschuwt je voor gevaren en zorgt ervoor dat je lichaam snel kan reageren op dat gevaar.
Soms is dat echter niet het geval. Je ervaart angst zonder dat daar een directe aanleiding voor, er is geen reëel gevaar aanwezig. Bijvoorbeeld wanneer je iemand moet opbellen, wanneer je in een lift staat of in een volle bus waar je niet zo snel weg kan. Wanneer de angst groot genoeg is, zal je de situaties waar je die angst voor voelt gaan vermijden.
The Digital Youth Project brings together young people and digital businesses to generate user insights. Founder Julia Shalet has developed innovative formats for real-world learning experiences. DYP has worked with clients like 02, BBC, and startups. DYP helps companies strengthen pitches, find user propositions, expedite product development, and review products. Case studies show how DYP helped clients win business, refine propositions, improve efficiency, and provide realistic feedback. DYP offers a practical, user-centric approach based on Julia Shalet's 15 years of product experience.
How to Become a Thought Leader in Your NicheLeslie Samuel
Are bloggers thought leaders? Here are some tips on how you can become one. Provide great value, put awesome content out there on a regular basis, and help others.
ON ALGORITHMIC PROBLEMS CONCERNING GRAPHS OF HIGHER DEGREE OF SYMMETRYFransiskeran
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.
On algorithmic problems concerning graphs of higher degree of symmetrygraphhoc
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.
FREQUENT SUBGRAPH MINING ALGORITHMS - A SURVEY AND FRAMEWORK FOR CLASSIFICATIONcscpconf
Data mining algorithms are facing the challenge to deal with an increasing number of complex
objects. Graph is a natural data structure used for modeling complex objects. Frequent subgraph
mining is another active research topic in data mining . A graph is a general model to represent
data and has been used in many domains like cheminformatics and bioinformatics. Mining
patterns from graph databases is challenging since graph related operations, such as subgraph
testing, generally have higher time complexity than the corresponding operations on itemsets,
sequences, and trees. Many frequent subgraph Mining algorithms have been proposed. SPIN,
SUBDUE, g_Span, FFSM, GREW are a few to mention. In this paper we present a detailed
survey on frequent subgraph mining algorithms, which are used for knowledge discovery in
complex objects and also propose a frame work for classification of these algorithms. The
purpose is to help user to apply the techniques in a task specific manner in various application domains and to pave wave for further research.
This document discusses various applications of graph theory to other areas of mathematics and other fields. It provides new graph theoretical proofs of Fermat's Little Theorem and the Nielsen-Schreier Theorem. It also discusses applications to problems in DNA sequencing, computer network security, scheduling, map coloring, and mobile phone networks. Specific algorithms for finding minimum vertex covers, vertex colorings, and matchings in graphs are applied to solve problems in these areas.
Graph terminology and algorithm and tree.pptxasimshahzad8611
This document provides an overview of key concepts in graph theory including graph terminology, representations, traversals, spanning trees, minimum spanning trees, and shortest path algorithms. It defines graphs, directed vs undirected graphs, connectedness, degrees, adjacency, paths, cycles, trees, and graph representations using adjacency matrices and lists. It also describes breadth-first and depth-first traversals, spanning trees, minimum spanning trees, and algorithms for finding minimum spanning trees and shortest paths like Kruskal's, Prim's, Dijkstra's, Bellman-Ford and A* algorithms.
Graph theory concepts complex networks presents-rouhollah nabatinabati
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.
Graphs can be represented using adjacency matrices or adjacency lists. Common graph operations include traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). DFS traverses a graph in a depth-wise manner similar to pre-order tree traversal, while BFS traverses in a level-wise or breadth-first manner similar to level-order tree traversal. The document also discusses graph definitions, terminologies, representations, elementary graph operations, and traversal methods like DFS and BFS.
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ALEXANDER FRACTIONAL INTEGRAL FILTERING OF WAVELET COEFFICIENTS FOR IMAGE DEN...sipij
The present paper, proposes an efficient denoising algorithm which works well for images corrupted with
Gaussian and speckle noise. The denoising algorithm utilizes the alexander fractional integral filter which
works by the construction of fractional masks window computed using alexander polynomial. Prior to the
application of the designed filter, the corrupted image is decomposed using symlet wavelet from which only
the horizontal, vertical and diagonal components are denoised using the alexander integral filter.
Significant increase in the reconstruction quality was noticed when the approach was applied on the
wavelet decomposed image rather than applying it directly on the noisy image. Quantitatively the results
are evaluated using the peak signal to noise ratio (PSNR) which was 30.8059 on an average for images
corrupted with Gaussian noise and 36.52 for images corrupted with speckle noise, which clearly
outperforms the existing methods.
Skiena algorithm 2007 lecture10 graph data strctureszukun
This document summarizes different types of graph data structures and representations. It discusses graphs as consisting of vertices and edges, and describes properties like directed vs undirected, weighted vs unweighted, sparse vs dense. It also covers different representations like adjacency matrices and lists, and provides code examples for initializing, reading, and inserting edges into a graph represented using an adjacency list.
Introduction to Graphs
Topics:
Definition: Graph
Related Definitions
Applications
Teaching material for the course of "Tecniche di Programmazione" at Politecnico di Torino in year 2012/2013. More information: http://bit.ly/tecn-progr
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It is well known that the tenacity is a proper measure for studying vulnerability and reliability in graphs.
Here, a modified edge-tenacity of a graph is introduced based on the classical definition of tenacity.
Properties and bounds for this measure are introduced; meanwhile edge-tenacity is calculated for cycle
graphs and also for complete graphs.
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.
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The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric → + Gd
: X × X × X R where X = r(v /W) =
{(d(v,v1
),d(v,v2
),...,d(v,vk
/) v∈V (G))}, denoted Gd
and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if Gd
numbers of pendant edges are added to the non-basis vertices.
Let G= (V, E) be a graph with p vertices and q edges. A graph G={V, E} with p vertices
and q edges is said to be a Permutation labelling graph if there exists a bijection function f
from set of all vertices
V G( )
to
{1, 2,3... }p such that the induced edge labelling function
h E G N : ( ) → is defined as
( ) ( ) 1 2 1 ( 2 )
,
f x h x x f x P =
or
( ) 2 f x( 1 )
f x P according as
f x f x ( 1 2 ) ( ) or
f x f x ( 2 1 ) ( ) where P is the permutation of objects( representing the
labels assigned to vertices). We in this paper have identified (m,n) Kite graph and attached
an edge to form a join to the kite graph and proved that the joins of (m,n) kite graphs is
permutation labelling graph and also have obtained some important results connecting the
joins of a (m,n) kite graph.
Cs6660 compiler design november december 2016 Answer keyappasami
The document discusses topics related to compiler design, including:
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Similar to Algorithm for Edge Antimagic Labeling for Specific Classes of Graphs (20)
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
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'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
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cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
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In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
How to Make a Field Mandatory in Odoo 17Celine George
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A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
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This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Algorithm for Edge Antimagic Labeling for Specific Classes of Graphs
1. Nissankara Lakshmi Prasanna & Nagalla Sudhakar
International Journal of Experimental Algorithms (IJEA), Volume (5) : Issue (1) : 2015 1
Algorithm for Edge Antimagic Labeling for Specific Classes of
Graphs
Nissankara Lakshmi Prasanna prasanna.manu@gmail.com
Research scholar of ANU & Asst.professor of Vignan’s
Lara Institution of Technology and Science/CSE
Guntur, India
Nagalla Sudhakar suds.nagalla@gmail.com
Professor & Principal of Bapatla Engineering College/CSE
Guntur, India
Abstract
Graph labeling is a remarkable field having direct and indirect involvement in resolving numerous
issues in varied fields. During this paper we tend to planned new algorithms to construct edge
antimagic vertex labeling, edge antimagic total labeling, (a, d)-edge antimagic vertex labeling, (a,
d)-edge antimagic total labeling and super edge antimagic labeling of varied classes of graphs
like paths, cycles, wheels, fans, friendship graphs. With these solutions several open issues
during this space can be solved.
Keywords: Graph Labeling, Edge Antimagic Vertex Labelling, Edge Antimagic Total Labelling,
Super Edge Antimagic Labelling, Paths, Cycles, Fan Graphs, Wheels, Friendship Graphs.
1. INTRODUCTION
A graph G = (V, E) is finite, straightforward and un-directed. G denotes graph then G includes a
vertex and edge sets. Vertex set denoted by V = V (G) and edge set E = E (G). We followed the
standard notations m = |E| and n = |V|. A typical graph theoretical notation is followed refer [13].
Labelled graphs are getting associate more and more helpful family of Mathematical Models for a
broad vary of applications [4, 17]. It’s terribly crucial impact in network communications explained
in [5]. Several latest applications presented its usage to image authentication and frequency
allocation.
Graph Labeling is a method of mapping that maps several set of elements of graph to a collection
of numbers (usually +ve or non -ve integers). The foremost complete graph labeling latest survey
is in [3] [14]. Sedlacek [9] introduce labelings that simplify the thought of a magic labeling. The
magic labelings is outlined as a bijection of graph component to set of successive integers
ranging from one, satisfying some reasonably “constant sum” property. If this Bijection involves
vertices or edges or both as graph elements to a collection of integers yielding a constant sum
known as magic constant, it'll be known as Vertex or Edge or Total Magic Labeling. Hartsfield
along with Ringel in [6] introduced the idea of an Antimagic graphs. In step with them associate
Antimagic labeling is a process of edge labeling of the graph with integers 1,2,…., m in order that
weight at every vertex is totally different from the weight at every vertex.
In [7] Bodendiek with Walter outlined the thought of an (a, d)-Antimagic labeling as edge labeling
during which the weights of vertex from an AP(arithmetic progression) ranging from a and have
common distinction d. Martin Baca, Francois Bertault and MacDougall [8] initiated the notions of
the Vertex Antimagic Total Labeling [VATL] and (a, d)-Vertex Antimagic Total Labeling [(a, d)-
VATL], and conjuncture that every regular graphs are (a, d)- VATL. In the year 2004, K.A.Sugeng
et al. [10] presented the concept of SVMTL (super vertex magic total labeling) & SEMTL (super
edge magic total labeling ). The existence of In [11] Antimagic vertex labeling of categories of
hyper graphs like Cycles, Wheels and therefore the existence and non-existence of the Antimagic
2. Nissankara Lakshmi Prasanna & Nagalla Sudhakar
International Journal of Experimental Algorithms (IJEA), Volume (5) : Issue (1) : 2015 2
vertex labeling of Wheels are mentioned in theorems. An idea to get antimagic labeling for trees
given in [12]. In reference [2] they projected the procedure (algorithms) to build (a, d)-Antimagic
labeling, Antimagic labeling, (a, d)-vertex Antimagic total labeling of complete graphs and vertex
Antimagic total labeling that could be a generalization of many different kinds of labelings.
In [15], we deal with the magic labeling of vertices and edges of a graph. Again magic labeling is
expressed in-terms of Vertex Magic Total Labeling (VMTL), Edge Total Magic Labeling (EMTL)
and Total Magic Labeling (TML). We have studied existing approaches for magic labeling and we
found some improvements can be done over existing VMTL algorithms and we design algorithm
to find EMTLs. We proposed new and enhanced algorithms for VMTL, EMTL and TML. We
applied these algorithms on different kinds of graphs like cycles, wheels, fans and friendship
graphs. In[16] we proposed new algorithms to construct vertex antimagic edge labeling, (a, d)-
vertex antimagic labeling, vertex antimagic total labeling and (a, d)-vertex antimagic total labeling
and super vertex-antimagic total labeling of various classes of graphs like paths, cycles, wheels,
Fan Graph and Friend Graphs.
In continuation to this, we have projected algorithms for EATL (Edge Antimagic Total labeling) on
different categories of graphs like cycles, paths, wheels, and fan and Friendship graphs. These
algorithms are similar all categories with minor changes because of structural variations. With
these we have to study the behaviour of the graphs with specific graph size. For given Graph with
size we will determine the attainable labelings, possible values of a and d to create (a, d) Edge
opposed magic Total Labelings and also the chance of forming SEMTL (super edge magic total
labeling).
2. PRELIMINARIES
Standard definitions of paths and wheels and cycles, fan and Friendship graphs are as follows. A
Path (Pn) could be a cycle without an edge from initial vertex to final vertex. Cycle could be a
graph wherever there's an edge amid the neighbouring vertices solely and therefore the vertex is
adjacent to final one (Fig1a). Wheel could be a Cycle with central hub, wherever all vertices of
cycle are neighbouring to that (Fig1b) Fans & Friendship graphs are variations of wheels. If a
path is linked to central hub it's a Fan (Fig1c). A Friendship graph has n triangles with 1 common
vertex known as hub and n is size of Friendship graph (Fig 1d)
FIGURE 1a: Path (P4)
FIGURE 1b:
Cycle(C4)
FIGURE 1c:
Wheel(W4)
FIGURE 1d:
Fan Graph(F4)
FIGURE 1e:
FriendshipGraph(T2)
Labeling is the method of distribution integers to graph elements is often called as a mapping
function from integers to Elements of Graph. Magic Labeling is outlined as a bijection from {1, 2,
3, 4, 5… n-1,n} to n - graph elements such the total of every element could be a magic constant
K . If the element is vertex or edge or both it's referred to as Vertex or Edge or Total magic Total
Labeling.
Let a G be a Graph with vertices v and edges e if there's a 1 to 1 function from set of integers
{1,2,3…..,n-2,n-1,n} to edges of Graph & vertices are appointed label as total of edges incident to
that. If the edge weights are completely different then it'll be EAVL ( Edge Antimagic Vertex
3. Nissankara Lakshmi Prasanna & Nagalla Sudhakar
International Journal of Experimental Algorithms (IJEA), Volume (5) : Issue (1) : 2015 3
Labeling) .For any 2 integers a, d if the sides are assign with labels is { a , a + d ,…..…. , a+(e-
1)d }, where a is greater than 0 i.e. a>0 and d greater than equal to 0 d>=0 is termed (a, d)
EATL. If the vertices are appointed with then successive numbers then, it'll be SEATL (Super
Edge Antimagic Labeling).
Likewise for a G graph with vertices V and edges E if there's a 1 to 1 operate from set of
integers {1,2,3,4,…………, v + e} to vertex set V & edge set E of graph and edge weight is total
of labels appointed to edge & labels appointed to its (V) vertices . If edge weights completely
different then it'll be Edge Antimagic Total Labeling (EATL). For any 2 integers a, d if the
vertices appointed with labels then , wherever a is greater than 0 i.e. a>0 and d greater than
equal to 0 d>=0 is termed as (a, d) EATL. If the vertices are indicated with successive numbers
then, it'll be Super Edge Antimagic Total Labeling (SEATL). Following section provides procedure
to spot above all for various topologies of Graphs. Accumulative variety of all such potentialities is
calculated. And open issues are solved & observed properties of graphs
3. PROPOSED WORK
During this section we have a tendency to discuss algorithmic rules to spot varied features of
edge Antimagic labeling. We have a tendency to offer generalized algorithmic rule in common to
any or all forms of Graphs mentioned during this paper. As a result of topological variations every
graph structure needs some modifications to algorithmic rule.1st we have a tendency to discuss
algorithmic rule then needed changes for every kind of graph are given during this section. the
subsequent functions are utilized in designing algorithmic rule.
npx : Generates various sizes x from set of n to set of numbers that are obtainable and unused
labels.
is_Duplicate (array, size) : The function returns Boolean value if array have duplicate values other
wise false
is_RegDiff (array, size) : The functions returns change of rate if the array have adjacent values
along with a common difference given by AP else it returns negative one (-).
is_SEATL ( array) : The function returns Boolean value if is_RegDiff (array, size) function returns
true then it also returns true otherwise false
Input : Graph G with vertices V & Edges E
Output : Possible variety of total Edge Anti Magic Vertex Labeling, Edge Anti Magic Vertex
Labeling, (a, d) Edge Anti Magic Vertex Labeling with a, d values, Total Edge Anti Magic Total
Labeling, Edge Anti Magic Total Labeling, (a, d) Edge Anti Magic Total Labeling with a, d values
and checks existence of super Edge Antimagic Labeling
Algorithmic procedure for EAVL
Read Graph with size n & set labels range {1,2,3,4….,r}.
for (i=1; i<=r ;i++)
If there exist rPn & it’s not an isomorphic then set them as labels of hub and spokes.
for (j=1;j<=r;j++)
if there exist rPn, then continue process
Otherwise display “all possible assignments are checked”.
Set them as labels of edges.
For all edges calculate weight.
Wei_ght[e] = addition of labels of its vertices.
If( is_Duplicate(wei_ght, n)) EAVL_cnt++;
Set d= is_RegDiff(wei_ght, n)
If(d>=1) adEAVL_cnt++;
If(d==1) SEAVL_cnt++;
Stop.
4. Nissankara Lakshmi Prasanna & Nagalla Sudhakar
International Journal of Experimental Algorithms (IJEA), Volume (5) : Issue (1) : 2015 4
Algorithm for EATL
Read Graph with size n and set labels range {1,2,3,4,5….r}.
For(i=1;i<=r;i++)
If there exist rPn & it’s not an isomorphic then set them as labels of hub & spokes.
for (j=1;j<=r;j++)
if there exist ar rP3 then continue process.
Otherwise display “all possible assignments are checked”.
Link1: Set them as labels of last edge, 1st vertex and 1st edge.
Previous vertex=1 current vertex=2
for (i=1;i<=r;i++)
if there exist a rp2 then continue process
else go to Link1.
Link2: Set them as labels of current vertex and current edge.
Previous vertex=current vertex Current vertex= curr_vertex+1
If current vertex=n then go to Link2.
else
reset labels assigned to previous vertex as available.
Previous vertex=prev_vertex-1 Current vertex= curr_vertex-1
For all edges calculate weight.
Wei_ght[e] = addition of labels assigned to it and labels assigned to its vertices.
If ( is_Duplicate(wei_ght, n)) EATL_cnt++;
Set d= is_RegDiff(wei_ght, n)
If (d>=1) adEATL_cnt++;
If (d==1) SEATL_cnt++;
Stop.
Modifications to be done For Path:
For EAVL Range R is {1,2,.....n}.
For EATL Range R is {1,2,.....2n-1}.
We can avoid Step 2 for Paths and set label of first edge as zero.
Modifications to be done For Cycle:
For EAVL Range R is {1,2,.....n}.
For EAT Range R is {1,2,.....2n}.
We can avoid Step 2 for Cycle.
Modifications to be done For Wheel:
For EAVL Range R is {1,2,.....n+1}.
For EATL Range R is {1,2,.....3n+1}.
Modifications to be done For Fan Graph:
For EAVL Range R is {1,2,.....n}.
For EATL Range R is {1,2,.....3n}.
Set label of first edge as zero.
Modifications to be done For Friendship Graph:
For EAVL Range R is {1,2,.....2*n+1}.
For EATL Range R is {1,2,.....5n+1}.
Set labels of even edges as zero.
4. RESULTS
Here we tend to designed algorithms to supply additive variety of edge anti magic vertex or total
labelings. we tend to conjointly known doable variety of (a, d) EAVL or Edge anti magic total
labelings for various values of a and d. Also we tend to calculated so many of super Antimagic
labelings if exists. Many authors analyzed behaviour of a specific graph structure for a few a and
d values. However here these algorithms turn out all such sequence of arrangement of vertices
and edges labels. So, we will simply and visually perceive behaviour of any structure.
Observations made are as follows.
5. Nissankara Lakshmi Prasanna & Nagalla Sudhakar
International Journal of Experimental Algorithms (IJEA), Volume (5) : Issue (1) : 2015 5
Paths:
All paths of size n>=3 is Anti magic. For Associate in Nursing instance if the path size is eight
there are 6024 (EAVL) Edge anti magic vertex labelings are possible and it's 64 (a, d) Edge anti
magic vertex labelings and fifty six among them are super edge magic. It has (3, 2) and (6, 1)
Edge anti magic vertex labelings for several sequences. Paths with any length consists several
Edge anti magic total labelings. For instance the path with length five has 233520 Edge anti
magic total labelings. it's 4680 (a, d) Edge anti magic total labelings among 1840 are super. This
sort of study is often done on any path. for each path there's no (a, d)-EAT labeling with d > 6.
Cycles:
In cycles, all cycles with size >=3 is antimagic. These algorithmic rules are estimated for many
values of n. For n=5 it resulted thirty Edge anti magic vertex labelings. It also has 10 (a, d) Edge
anti magic vertex labelings for a few values of a and d and each one of those are super. For a
cycle of size five we tend to observed 1858600 Edge anti magic total labelings. It also has 10460
(a ,d) Edge anti magic total labelings among 4980 are super. feasible values of (a, d) are (6,5),
(7,5), (8,4)etc.
In the similar way we will analyze any cycle with any given size.
Wheels:
Wheel with size≥ three, has no edge magic vertex labeling. But it has edge magic total labelings.
For given wheel size we are able to show the attainable Edge anti magic total labelings. If the
wheel size is three, then there exist 1128768 Edge anti magic total labelings. It’s 4512 (a, d) Edge
anti magic total labelings for values among 3840 are super Edge anti magic total labelings. we've
got (15,1), (16,1), (17,1), (18,1), (10,3) and (11,3) etc attainable (a, d) Edge anti magic total
labelings
Fan Graphs:
Fan Graphs are Antimagic with size three to six. Although the number of such sequences are
very less all those are (a, d) Edge anti magic vertex labelings. Fan graphs with size three, four
and five are giving 8 (a, d) Edge Anti Magic Vertex Labelings however all are super Edge anti
magic vertex labelings & all are of (3,1) Edge anti magic vertex labelings. For Fan Graphs we
tend to indicate some shocking results. If the fan size is three, then there exist 152152 Edge anti
magic total labelings. It’s 1344(a, d) Edge anti magic total labeling for various values among 672
are super Edge anti magic total labelings. we've got (14,2),(9,3) ,(16,1),(8,3) (11,3), (15,1), (12,2)
and (11,3) etc attainable (a, d) Edge anti magic total labelings.
Friendship Graphs:
Friendship graph also has edge anti magic labeling. Friendship graphs also are observed as
every (a, d) edge anti magic vertex labeling is super. Friendship graph with size 2 is having 24
edge anti magic vertex labelings and none of them is (a, d) edge anti magic vertex labeling.
However Friendship graphs with size 1,3,4,5 are producing edge anti magic vertex labelings,(a,
d) edge anti magic vertex labelings. For these graphs all are super edge magic. Friendship graph
with size three producing 192 edge anti magic vertex labelings and 48 (a, d) edge anti magic
vertex labelings and every one area unit super. Friendship graph with size four manufacturing
3072 edge anti magic vertex labelings and 2304 (a, d) edge anti magic vertex labelings and all of
them are super edge anti magic vertex labelings. Each Friendship graph could be a super edge
anti magic total labeling. For Friendship graphs with size 3 has huge number of edge anti magic
total labeling (a, d) edge anti magic total labeling for d=2. These are some observations created
by us.
5. CONCLUSIONS
In this paper, we tend to provide algorithms to enumerate all Edge Antimagic labelings on wheel
graphs, Fan Graphs, cycle Graphs and Friendship graphs. The thought of the algorithms can be
applied to alternative categories of graphs or adopted to develop algorithms for other form of
labeling. within the in the meantime, we still engaged on algorithm for other form of labeling like
edge anti magic and total, harmonious, swish etc. we tend to present the number of non
6. Nissankara Lakshmi Prasanna & Nagalla Sudhakar
International Journal of Experimental Algorithms (IJEA), Volume (5) : Issue (1) : 2015 6
isomorphic completely different anti magic labelings on every graph for a some small size graphs.
The number of non-isomorphic labeling on larger size of the remaining graphs is still an open
problem.
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