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14 Sep 2017 Full-text (PDF) | Abstract. A fuzzy graph (f-graph) is a pair G : (s, ?) where s is a fuzzy subset of a set S and ? is a fuzzy relation on s. A fuzzy graph H : (t, u) is called a partial fuzzy subgraph of G : (s, ?) if t (u) ? s(u) for every u and u (u, v) ? ?(u, v) for every u and v . In particul
This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine's work on fuzzy interval graphs, fuzzy analogs of Marczewski's theorem, and the Gilmore and Hoffman characterization.
Definition 1.10. Let Vbe·a non empty set. A fuzzy graph is a pair of functions. ,--,/. G : (0; )1) where o is a fuzzy subset of V and .Jl is a symmetric fuzzy relation on a ·. i.e. a: V ~ [O,l} and J1: VxV ~ {O,l} such that J1 (u, v) ~ a (u) / a (v) for all u, v in. V. We denote the underlying (crisp) graph of G: (0; J1) by G* :(a*, fJ*) where a* is.
Abstract. Coloring of fuzzy graphs plays a vital role in theory and practical applications. The concept of chromatic number of fuzzy graphs was introduced by Munoz[6] et.al. Later Eslahchi and Onagh [7]defined fuzzy coloring of fuzzy graphs and defined fuzzy chromatic number ?f (G). Incorporating the features of these two
The de?nition of complement of a fuzzy graph is modi?ed and some properties of self complementary fuzzy graphs are studied. We show that automorphism groups of a fuzzy graph and its complement are identi?cal and a relative study of complement and some other operations on fuzzy graphs such as union, join and
22 Oct 2015 Also some properties of strongly edge irregular fuzzy graphs are studied and they are examined for strongly edge totally irregular fuzzy graphs. 1. Introduction. Euler first introduced the concept of graph theory in 1736. In 1965, Lofti A. Zadeh. [14] introduced the concept of a fuzzy subset of a set as a method
Abstract. A graph is a pair (V, R), where V is a set and R is a relation on V. 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 ? on a fuzzy subset ? of a set V can be regarded as defining a weighted graph, or fuzzy graph, where the edge (x,
1 Oct 2013 An f-graph G : (?, ?) is connected if for every x,y in ?* ,CONNG(x, y) > 0. In this paper, we offer a survey of selected recent results on fuzzy graphs. Keywords: Fuzzy graph, Strongest path, strong path, fuzzy cycle, fuzzy tree. AMS Mathematics Subject Classification (2010): 05C75. 1. Introduction. It is quite well
Keywords: Complete Fuzzy Graph, Fuzzy Total Coloring, Chromatic Number, Executive. Committee Problem. 1. Introduction: Graph coloring finds its origin during late 1850 and the term “total coloring" was independently introduced by Behzad and Vizing in numerous occasions between1964 and 1968. As graph theory has
Similarly. a fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. µ) where ? is a fuzzy subset of a set S and µ is a fuzzy relation on ?. y) not in F there exists a path from x to y in F whose strength is more than µ(x.org Fuzzy Graph Theory: A Survey M. The strength of connectedness between two nodes x and y is
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