Domination parameters and diameter of Abelian Cayley graphs

TL;DR

This paper investigates the total and connected domination numbers and the diameter of Abelian Cayley graphs constructed from specific direct product groups, providing new insights into their structural properties.

Contribution

It introduces new bounds and relationships for domination parameters and diameter in Abelian Cayley graphs based on group product structures.

Findings

Derived bounds for domination numbers.

Established relationships between diameter and group structure.

Provided new characterizations of Abelian Cayley graphs.

Abstract

Using the domination parameters of Cayley graphs constructed out of $\mathbb{Z}_{p}\times \mathbb{Z}_{m}$, where $m\in\{p^{\alpha}, p^{\alpha}q^{\beta}, p^{\alpha}q^{\beta}r^{\gamma}\},$ in this paper we are discussing about the total and connected domination number and diameter of these Cayley graphs.