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∈ V(G) D there is a vertex y∈ D with xy∈ E(G) and deg(x)≤ deg(y). The strong domination number γₛₜ(G) is defined as the minimum cardinality of a strong dominating set. In this paper, we calculate γₛₜ(G) for specific graphs and study the number of strong dominating sets of some graphs.