Changing and unchanging the Roman domination number of a graph

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 with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value f (V(G)) = Sigma(u is an element of v(G)) f(u). The Roman domination number gamma(G) of G is the minimum weight of a Roman dominating function on C. In this paper, we study how the Roman domination number changes by means of removing a vertex or an edge from a graph.