SOME RESULTS ON ROMAN DOMINATION EDGE CRITICAL GRAPHS

A Roman dominating function on a graph G with vertex set V(G) is a function f : V(G) -> {0, 1, 2} 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 a Roman dominating function f is the value f(V(G)) = Sigma(u is an element of v(G)) f(u). The Roman domination number, gamma(R)(G), of G is the minimum weight of a Roman dominating function on G. In this paper we continue the study of Roman domination edge critical graphs by giving several properties and characterizations for these graphs.