STRONG DOMINATION NUMBER OF HAJÓS SUM AND VERTEX-SUM OF TWO GRAPHS

Nima Ghanbari, Saeid Alikhani

DOI Number
https://doi.org/10.22190/FUMI230720032G
First page
469
Last page
479

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 $\gst(G)$ is defined as the minimum cardinality of a strong dominating set.  In this paper, we study the strong domination number of Haj\'{o}s sum and vertex-sum of two graphs.

Keywords

graph, strong domination number, Hajós sum.

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References


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DOI: https://doi.org/10.22190/FUMI230720032G

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