Strength of Fuzzy Domination in Fuzzy Graphs

Two vertices in a graph are said to dominate each other if they are adjacent. A set S of vertices in a graph G is a dominating set of G if every vertex is dominated by some vertex of S. In this paper we define a new type of strength of fuzzy domination in fuzzy graphs by fuzzy logic. Then we determine strength of fuzzy complete graphs and fuzzy complete bipartite graphs and some bounds for strength of fuzzy domination in fuzzy graphs are obtained. Also we define strength of fuzzy independent domination and strength fuzzy irredundant in fuzzy graphs. Finally we discuss some relations between these parameters.