Roman domination number of signed graphs

A function f : V-+ {0,1, 2} on a signed graph S = (G, sigma) where G = (V, E) is a Roman dominating function (RDF) if f(N[v]) = f(v) + E u is an element of N(v) sigma (uv)f (u) > 1 for all v E V and for each vertex v with f(v) = 0 there is a vertex u in N+(v) such that f (u) = 2. The weight of an RDF f is given by omega(f) = Ev is an element of V f(v) and the minimum weight among all the RDFs on S is called the Roman domination number-yR(S). Any RDF on S with the minimum weight is known as a-yR(S)-function. In this article we obtain certain bounds for-yR and characterise the signed graphs attaining small values for-yR.