On Commuting Graphs of Generalized Dihedral Groups

TL;DR

This paper investigates the properties of commuting graphs associated with generalized dihedral groups, providing insights into their structure and characteristics within group theory.

Contribution

It offers new analysis of the commuting graphs of generalized dihedral groups, expanding understanding of their structural properties.

Findings

Characterization of commuting graph connectivity

Identification of conditions for graph regularity

Insights into graph symmetry and automorphisms

Abstract

For a group $G$ and a subset $X$ of $G$, the commuting graph of $X$, denoted by $\Gamma(G,X)$ is the graph whose vertex set is $X$ and any two vertices $u$ and $v$ in $X$ are adjacent if and only if they commute in $G$. In this article, certain properties of the commuting graph of generalized dihedral groups have been studied.