Roman domination in signed graphs

Let $S = (G,sigma)$ be a signed graph. A function $f: V rightarrow {0,1,2}$ is a Roman dominating function on $S$ if $(i)$ for each $v in V,$ $f(N[v]) = f(v) + sum_{u in N(v)} sigma(uv ) f(u) geq 1$ and $(ii)$ for each vertex $ v $ with $ f(v) = 0 $ there exists a vertex $u in N^+(v)$ 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.