Fuzzy domination in fuzzy graphs

Let G = ( V, mu, sigma) be a fuzzy graph on a finite set V. A fuzzy subset mu' of mu is called a fuzzy dominating set of G if, mu' (nu) + Sigma(x is an element of v)(sigma( x, nu)Lambda mu'(x)) >= mu(nu) for every v.is an element of V. Fuzzy domination number.fz is defined accordingly. In this paper we initiate a study of this parameter. Some properties of fuzzy dominating sets are studied and fuzzy domination number.fz is determined for some graphs.

Automated summary

This paper studies the fuzzy dominating sets and their properties in fuzzy graphs, and determines the fuzzy domination number for some graphs.