On edge domination numbers of graphs

Let γs′(G) and γss′(G) be the signed edge domination number and signed star domination number of G, respectively. We prove that 2n-4⩾γss′(G)⩾γs′(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.