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.