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Recent Developments on the Basics of Fuzzy Graph Theory

Recent Developments on the Basics of Fuzzy Graph Theory
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Author(s): Ganesh Ghorai (Vidyasagar University, India) and Kavikumar Jacob (Universiti Tun Hussein Onn Malaysia, Malaysia)
Copyright: 2020
Pages: 18
Source title: Handbook of Research on Advanced Applications of Graph Theory in Modern Society
Source Author(s)/Editor(s): Madhumangal Pal (Vidyasagar University, India), Sovan Samanta (Tamralipta Mahavidyalaya, India) and Anita Pal (National Institute of Technology Durgapur, India)
DOI: 10.4018/978-1-5225-9380-5.ch018

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Abstract

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 fuzzy graph, complete and strong fuzzy graph, bipartite fuzzy graph, degree of a vertex in fuzzy graphs, fuzzy subgraph, etc. These concepts are illustrated with some examples. The recently developed concepts like fuzzy planar graphs are discussed where the crossing of two edges are considered. Finally, the concepts of fuzzy threshold graphs and fuzzy competitions graphs are also given as a generalization of threshold and competition graphs.

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