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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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