Electronic journal of graph theory and applications ejgta. Zadeh in 1965after zadeh many authors have extensively developed the theory of fuzzy sets and its application. Finally, this paper concludes that any preference graph is a fuzzy graph type 5. A subset s of v is called a dominating set in g if every vertex in vs is effectively adjacent to at least one vertex in s. Rosenfeld introduced the fuzzy analogue of several basic graph theoretic concepts and bhattacharya gave some remarks on fuzzy graphs. We introduce the notion of fuzzy rough digraphs and describe some of their methods of construction. Fuzzy graph is now a very important research area due to its wide application. Sc fuzzy set theory introduction fuzzy set theory fuzzy set theory is an extension of classical set theory where elements have varying degrees of membership. We introduce some definitions for fuzzy graphs and provide examples to explain various notions introduced. In this article, we introduce the notions of maximal products of fuzzy graph structures, regular fuzzy graph structures, and describe these notions with examples.
Not much have been studied theoretically on connectivity of normalized networks. Fuzzygraph structures are more useful than graph structures because they deal with the uncertainty and ambiguity of many realworld phenomena. International journal of pure and applied mathematics. A logic based on the two truth values, true and false, is sometimes inadequate when describing human reasoning. Extremal problems for hypergraph blowups of trees with z. A fuzzy set ain xis characterized by its membership function a. Fuzzy setbased techniques are also an important ingredient in the development of information technologies. Pdf some remarks on complement of fuzzy graphs iosr. Fuzzy graph coloring is one of the most important problems of fuzzy graph theory. We investigate isomorphism properties of antipodal interval valued fuzzy graphs. New approach on regular fuzzy graph research india publications.
Mathematics free fulltext fuzzy graph structures with application. Tree set theory need not be a tree in the graphtheory sense, because there may not be a unique path between two vertices tree descriptive set theory euler tour technique. In this chapter, the authors introduce some basic definitions related to fuzzy graphs like directed and undirected fuzzy graph, walk, path and circuit of a. Papers with pdf links to recent ones submitted comments are welcome cliques with many colors in triple systems with a. See glossary of graph theory terms for basic terminology examples and types of graphs. The number of vertices in a largest clique of g is called the clique number of g. His current research topics include fuzzy graph theory, biocomputational modeling, graph theory, fractal geometry, and chaos. Citescore values are based on citation counts in a given year e. Theory of fuzzy graphs definitions and basic concepts. Ramakrishnan and dinesh 2325 worked on generalized fuzzygraph structures.
The journal of graph theory is devoted to a variety of topics in graph theory, such. Mathew on blocks and stars in fuzzy graphs 1665 5 k. This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. Samanta and pal introduced fuzzy tolerance graphs 21, fuzzy threshold graphs 22, fuzzy competition graphs 23 and bipolar fuzzy hypergraphs 24.
After rosenfeld 20, fuzzy graph theory is increased with a large number of branches. It introduces readers to fundamental theories, such as craines work on fuzzy interval graphs, fuzzy analogs of marczewskis theorem, and the gilmore and hoffman characterization. Harinath and lavanya discussed fuzzy graph structures for wheel, helm, and star graphs 26. Further, we define what we mean by an ordered fuzzy graph, a complete fuzzy graph and show that every fuzzy group can be embedded in a fuzzy group of the group of automorphisms of some fuzzy graph. Recall that a fuzzy relation on a set s 2 is a fuzzy subset of s x s, that is, a map. Fuzzy rough set theory is a hybrid method that deals with vagueness and uncertainty emphasized in decisionmaking. In the field of information processing fuzzy sets are important in clustering, data analysis and data fusion, pattern recognition and computer vision. Let g v, e be a graph where v nonempty set is called vertex set and e is called edge set. Furthermore, we determine the fuzzy chromatic polynomials for some fuzzy graphs with crisp and fuzzy vertices.
Fuzzy colouring of mpolar fuzzy graph and its application. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including and not restricted to aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. The global connected domination in fuzzy graphs dr. Mathematics free fulltext fuzzy graph structures with. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including and not restricted to aggregation operations, a generalized theory of relations, specific measures of. The notion of fuzzy topology on fuzzy sets was introduced by chakraborty and ahsanullah 1 as one of treatments of the problem which may be called the subspace problem in fuzzy topological spaces. In this section, we shortly recalled some basic definitions of undirected graphs, mpolar fuzzy graphs and other terms related to it. The properties of fuzzy graphs have been studied by azriel rosenfeld7. Fuzzy rough graph theory with applications atlantis press. In the mathematical discipline of graph theory, a wheel graph wn is a graph with n vertices n. Harinath and lavanya discussed fuzzy graph structures for wheel, helm, and star graphs. Thenotionsoffuzzysoftgraph,union,intersectionoftwo.
Recent developments on the basics of fuzzy graph theory. A fuzzy set a defined on a non empty set x is the family ax, a x. The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. Ma 8151 fuzzy graph theory and applications prerequisite. Fuzzy vertex graceful labeling on wheel and fan graphs. Fuzzy chromatic polynomial of fuzzy graphs with crisp and. Fuzzy chromatic polynomial of fuzzy graphs with crisp and fuzzy. In this article, we introduce the notions of maximal products of fuzzy graph structures, regular fuzzy graph structures, and describe these notions with examples and properties. Myna, abstract in this paper, we use a fuzzy graph model to represent a traffic network of a city and discuss a method to find the different type of accidental zones in a traffic flows using edge coloring of a fuzzy graph. Most of the research works available in the literature have been restricted to an algorithmic perspective alone.
Vijayakumar, blocks in fuzzy graphs, the journal of fuzzy. Now, in this paper, some types of t fuzzy graphs an considered, fuzzy adjacency matrix of that t fuzzy graphs is obtains. Fuzzy graph theory is finding numerous application in the fields of information theory, neural networks. Rosenfeld, fuzzy end nodes in fuzzy graphs, information sciences 152 2003, 323326. In particular, we consider applications of fuzzy rough. The relation connected is a reflexive, symmetric and transitive, the equivalence classes of nodes under this relation are the connected components of the given fuzzy graph. The elements of v are thought of as vertices of the graph and the elements of r are thought of as the edges similarly, any fuzzy relation. Corresponding authors with email addresses will be sent page proofs and instructions in pdf format via email.
He is a member of several academic bodies and associations. A very close association of fuzzy planar graph is fuzzy dual graph. Ramakrishnan and dinesh 23,24,25 worked on generalized fuzzy graph structures. The journal of graph theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs.
In this research study, we apply the concept of fuzzy rough sets to graphs. Advanced topics in fuzzy graph theory john mordeson springer. If no edge incident with a vertex, then the vertex is said to be isolated vertex, otherwise, it is said to be nonisolated vertex. A fuzzy graph is called highly irregular 16 if every vertex of g is adjacent to vertices with distinct degrees. One of the advantages of defining topology on a fuzzy set lies in the fact that subspace topologies can now be developed on fuzzy subsets of a fuzzy.
Fuzzy graph theory answers to most of the problems in this area. This book discusses fundamental concepts and recent developments in fuzzy graphs in. Fuzzy graph model for assignment problem 163 this assignment problem can be solved by finding a complete matching of fuzzy bipartite graph of g. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. Concept of fuzzy planar graphs ieee conference publication. But normalization of weights are necessary to deal with large size networks like internet. Fuzzy graph structures are more useful than graph structures because they deal with the uncertainty and ambiguity of many realworld phenomena. Applications in engineering and technology is to foster advancements of knowledge and help disseminate results concerning recent applications and case studies in the areas of fuzzy logic, intelligent systems, and webbased applications among working professionals and. The total degree of a index terms fuzzy graph, direct sum, effective fuzzy graph, regular fuzzy graph, connectedness, upper and lower truncations. Journal of graph theory author guidelines wiley online. In order to expedite the publication and online posting of articles in wiley online library, the journal of graph theory now offers electronic proofing. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. The theory ofgraphisextremelyusefultoolforsolvingcombinatorialproblemsindif ferentareassuchasgeometry,algebra,numbertheory,topology,operation research, optimization and computer science, etc in 1975, rosenfeld 2 introduced the concept of fuzzy graphs. First let us recall some preliminary definitions that can be found in 19.
Antipodal interval valued fuzzy graph, median interval valued fuzzy graph, status. Fuzzy rulebased modeling has been combined with other techniques such as neural nets. Rosenfeld introduced the fuzzy analogue of several basic graphtheoretic concepts and bhattacharya gave some remarks on fuzzy graphs. Pdf the concept of an antipodal bipolar fuzzy graph of a given bipolar fuzzy graph is. International journal of fuzzy computation and modelling. The journal brings together the leadingedge research on fuzzy set theory, fuzzy logic, soft computing and related topics to present original research of high quality. The electronic journal of graph theory and applications ejgta is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. Furthermore, we develop a flowchart to show general. This is a list of graph theory topics, by wikipedia page. This article gives a survey of the fundamentals of fuzzy set theory and describes potential applications. In this paper, vertex regular fuzzy graph, total degree and totally vertex regular fuzzy graph are. Applications of fuzzy set theory 9 9 fuzzy logic and approximate reasoning 141 9. Introduction uzzy graph theory was introduced by azriel rosenfeld in 1975.
For any fuzzy graph g a complete sub fuzzy graph of g is called a clique of g. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a. Further, we present the degree and total degree of a vertex in maximal product of fuzzy graph structures and explain some of their properties. In this paper, we define both of these graphs and studied a lot of properties. Since its launching in 1978, the journal fuzzy sets and systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems.
Fuzzy graph g v, e is a non empty set v together with a pair of function a. Applications in engineering and technology is to foster advancements of knowledge and help disseminate results concerning recent applications and case studies in the areas of fuzzy logic, intelligent systems, and webbased applications among working professionals and professionals in education and research. In 1975 rosendfeld 4 and yeh and beng 10 independently developed the theory of fuzzy graph. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic cycle. Fuzzy multigraph and fuzzy planar graphs are two subclasses of fuzzy graph theory. Advances in fuzzy systems provides an international forum for original research articles in the theory and applications of fuzzy subsets and systems. A graph is a pair v, r, where v is a set and r is a relation on v.
Ijfcm includes theoretical, experimental and applications of fuzzy mathematics and computation in general. Triangles in graphs without bipartite suspensions with s. Research article intuitionistic fuzzy planar graphs. We show that every fuzzy group can be imbedded in a fuzzy group of the group of automorphisms of some fuzzy graph. This book provides a timely overview of fuzzy graph theory, laying the foundation for. He has an experience of 20 years in teaching and research. Fuzzy set theoryand its applications, fourth edition.
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