Roman domination in signed graphs

Let S = (G, sigma) be a signed graph. A function f : V -> {0; 1; 2} is a Roman dominating function on S if (i) for each v is an element of V; f(N[v]) = f(v)+ Sigma(u is an element of N(v)) sigma(uv)f(u) >= 1 and (ii) for each vertex v with f(v) = 0, there exists a vertex u is an element of N+(v) such that f(u) = 2. In this paper we initiate a study on Roman dominating function on signed graphs. We characterise the signed paths, cycles and stars that admit a Roman dominating function.