Domination related parameters in rooted product graphs

TL;DR

This paper investigates various domination parameters in rooted product graphs, providing insights into how these parameters behave and can be characterized within this specific class of graph products.

Contribution

It introduces new results on domination parameters in rooted product graphs, expanding understanding of their properties and potential applications.

Findings

Derived bounds for domination parameters in rooted product graphs

Characterized domination sets in specific rooted product graph classes

Extended existing domination theory to rooted product graph structures

Abstract

A set $S$ of vertices of a graph $G$ is a dominating set in $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. A domination parameter of $G$ is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of $G$. Here, we investigate several domination related parameters in rooted product graphs.