Strong domination number of a modified graph

Document Type : Original Article

Authors

1 Department of Mathematical Science, Yazd University, 89195-741, Yazd, Iran

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

Abstract

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 $G$.

Keywords

References

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AUT Journal of Mathematics and Computing
Volume 5, Issue 3
July 2024
Pages 217-223

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