ON THE STRONG DOMINATING SETS OF GRAPHS
نویسندگان
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.
3 Department of Mathematical Sciences, Yazd University, P.O. Box 89195-741, Yazd, Iran.
doi
10.22044/jas.2022.11646.1595چکیده
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.
