ROMAN DOMINATION ON SOME GRAPHS.

Let G = (V, E) be a graph. A Roman dominating function (RDF) f : V {0,1,2} in 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. The weight of an RDF f is f(V) = _∑ue f (v). The Roman domination number of a graph G, denoted by yr(G), is the minimum weight of an RDF on G. In this paper, the Roman domination numbers of some graphs are given. [ABSTRACT FROM AUTHOR]