Independent Restrained k - Rainbow Dominating Function

Abstract

Let G be a graph and let f be a function that assigns to each vertex a set of colors chosen from the set {1, 2…, k} that is f: V(G)  P [1,2,…,k]. If for each vertex v  V(G) such that f(v) =  .we have  then f is called the k – Rainbow Dominating Function (KRDF) of G. A k – Rainbow Dominating Function is said to be Independent Restrained k - Rainbow Dominating function if (i)The set of vertices assigned with non – empty set is independent. (ii)The induced subgraph of G, by the vertices with label   has no isolated vertices. The weight w(f) of a function f is defined as w(f) =  .The Independent Restrained k – Rainbow Domination number is the minimum weight of G. In this paper we introduce Independent Restrained k – Rainbow Domination and find for some graphs