Strong domination number of some operations on a graph

Alikhani, Saeid; Ghanbari, Nima; Zaherifar, Hassan

doi:10.22049/cco.2023.28649.1652

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	Strong domination number of some operations on a graph
Communications in Combinatorics and Optimization
مقاله 11، دوره 9، شماره 4، اسفند 2024، صفحه 773-783 اصل مقاله (420.81 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2023.28649.1652
نویسندگان
Saeid Alikhani^* ¹؛ Nima Ghanbari²؛ Hassan Zaherifar¹
¹Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran
²Department of Informatics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway
چکیده
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 examine the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on edge (or edges) of $G$.
کلیدواژه‌ها
edge deletion؛ edge subdivision؛ edge contraction؛ strong domination number

مراجع
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Strong domination number of some operations on a graph