On edge domination numbers of graphs

Let @c"s^'(G) and @c"s"s^'(G) be the signed edge domination number and signed star domination number of G, respectively. We prove that 2n-4>[email protected]"s"s^'(G)>[email protected]"s^'(G)>=n-m holds for all graphs G without isolated vertices, where n=|V(G)|>=4 and m=|E(G)|, and pose some problems and conjectures.