Strong domination number of a modified graph

Document Type : Original Article

Authors

1 Department of Mathematical Sciences, 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 $\gamma_{st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{st}(G)$ when $G$ is modified by operations on vertices and edges of $G$.

Keywords

AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 10 August 2023

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