Fuzzy Double Domination Number and Chromatic Number of a Fuzzy Graph

A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to at least one vertex in S. A Dominating set is said to be Fuzzy Double Dominating set if every vertex in V-S is adjacent to at least two vertices in S. The minimum cardinality taken over all, the minimal double dominating set is called Fuzzy Double Domination Number and is denoted by γ fdd (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 χ(G). For any graph G a complete subgraph of G is called a clique of G. In this paper we find an upper bound for the sum of the Fuzzy Double Domination Number and Chromatic Number in fuzzy graphs and characterize the corresponding extremal fuzzy graphs.