Restrained roman domination in graphs

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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.