Different Types of Dominating Critical in Fuzzy Graphs

Abstract

Let G: (σ, μ) be a fuzzy graph. A set D of V is said to be fuzzy dominating set of G if every v ε V-D there exit u ε D such that u dominates v. Let u and v be any two vertices of a fuzzy graph G. Then u strongly dominates v (v weakly dominates u) if (i) μ (u, v) = σ (u) σ(v) and (ii) d N (u) ≥ d N (v).Let G be a fuzzy graph. Then D V is said to be a strong (weak) fuzzy dominating set of G if every vertex v є V − D is strongly (weakly) dominated by some vertex u in D. In this paper we investigate the changes in the fuzzy cardinality of above dominating sets, when we remove the vertex in the graph G.