Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 5 3 2024 07 01 Strong domination number of a modified graph 217 223 5207 10.22060/ajmc.2023.22327.1152 EN Saeid Alikhani Department of Mathematical Science, Yazd University, 89195-741, Yazd, Iran Nima Ghanbari Department of Informatics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway Journal Article 2023 04 10 Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gamma_{\rm st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{\rm st}(G)$ when $G$ is modified by operations on vertices and edges of $G$. https://ajmc.aut.ac.ir/article_5207_246a3c5544feb054f3ea718f61adfa16.pdf