on the strong dominating sets of graphs

let g = (v (g);e(g)) be a simple graph. a set d v (g) is a strong dominating set of g, if for every vertex x 2 v (g) n d there is a vertex y 2 d with xy 2 e(g) and deg(x) deg(y). the strong domination number st(g) is defined as the minimum cardinality of a strong dominating set. in this paper, we calculate st(g) for specific graphs and study the number of strong dominating sets of some graphs.