Characterisation of Restrained 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 adjacent to at least one vertex in S. A subset S of V is said to be a restrained dominating set if every vertex in V-S is adjacent to atleast one vertex in S as well as adjacent to atleast one vertex in V-S. The restrained domination number of a fuzzy graph (, ,)is denoted by (G) which is the smallest cardinality of a restrained 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 Restrained domination and chromatic number in fuzzy graphs and characterize the corresponding extremal fuzzy graphs.
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