Study on strength of strongest dominating sets in fuzzy graphs

A set S of vertices in a graph G =(V.E) is a dominating set of G if every vertex of V - S is adjacent to some vertex of S. A set S of vertices is an exact k-step dominating set if any vertex of G is at distance k from exact one vertex of S. In this paper, at the first we study on the strength of strongest 2-step dominating set in 2-corona fuzzy graphs and then we study on dominating set in fuzzy graphs especially fuzzy paths and fuzzy cycles.Then we introduce the concepts of strength of strongest dominating set in complement of fuzzy graphs.