Document Type : Original Manuscript


1 Department of Mathematical Sciences, Yazd University, P.O. Box 89195-741, Yazd, Iran.

2 Department of Informatics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway.


Let $G=(V(G),E(G))$ be a simple graph. A set $D\subseteq V(G)$ is a strong dominating set of $G$, if for every vertex $x\in V(G)\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we calculate $\gamma_{st}(G)$ for specific graphs and study the number of strong dominating sets of some graphs.


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