On the signed star domination number of regular multigraphs

Let $G$ be a graph with the vertex set $V(G)$ and the edge set $E(G)$ . A function $f: E(G)longrightarrow {-1, 1}$ is said to be a signed star dominating function of $G$ if $sum _{e in E_G(v)}f (e)ge 1 $ , for every $v in V(G)$ , where $E_G(v) = {uvin E(G),|,u in V (G)}$ . The minimum values of $sum _{e in E_G(v)}f (e)$ , taken over all signed star dominating functions $f$ on $G$ , is called the signed star domination number of $G$ and denoted by $gamma _{SS}(G)$ . In this paper we determine the signed star domination number of regular multigraphs.