Restrained roman domination in graphs

A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. A set S V is a Restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in. We define a Restrained Roman dominating function on a graph G = (V,E) to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and at least one vertex w for which f(w) = 0. The weight of a Restrained Roman dominating function is the value. The minimum weight of a Restrained Roman dominating function on a graph G is called the Restrained Roman domination number of G and denoted by. In this paper, we initiate a study of this parameter.