Strong domination number of Haj\'{o}s sum and vertex-sum of two graphs

TL;DR

This paper investigates the properties of the strong domination number in graphs formed by Hajós sum and vertex-sum operations, providing insights into their domination characteristics.

Contribution

It introduces the concept of strong domination number for Hajós sum and vertex-sum of graphs, analyzing their properties and bounds.

Findings

Derived bounds for strong domination number in Hajós sum

Analyzed strong domination number in vertex-sum of graphs

Provided theoretical results on domination properties

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 strong domination number of Haj\'{o}s sum and vertex-sum of two graphs.