Independent Domination Number and Chromatic Number of a Fuzzy Graph

Let be a simple undirected fuzzy graph. A subset S of V is called a dominating set in G if every vertex in V-S is effectively adjacent to at least one vertex in S. A dominating set S of V is said to be a Independent dominating set if no two vertex in S is adjacent. The independent domination number of a fuzzy graph is denoted by (G) which is the smallest cardinality of a independent dominating set of G. The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number (G). For any fuzzy graph G a complete fuzzy sub graph of G is called a clique of G. In this paper we find an upper bound for the sum of the independent domination and chromatic number in fuzzy graphs and characterize the corresponding extremal fuzzy graphs.