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.