h. r. maimani

For a graph G=(V, E) of order n, a Roman {2}-dominating function f: V→E has the property that for every vertex v in V with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to least two vertices assigned 1 under f. In this paper, we classify all graphs with Roman {2}-domination number belonging to the set {2, 3, 4, n-2, n-1, n}. Furthermore, we obtain some results about Roman {2}-domination number of some graph operations.