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.