Abelian covers of alternating groups

TL;DR

This paper investigates the properties of the commuting graph of alternating groups, specifically analyzing the relationship between independence number and clique-covering number for most values of n.

Contribution

It provides a comprehensive analysis of the commuting graph of alternating groups, identifying cases where the independence number equals the clique-covering number, excluding specific values of n.

Findings

For all n except 13, 14, 17, and 19, the independence number equals the clique-covering number in the commuting graph of A_n.

The paper characterizes the structure of the commuting graph for alternating groups.

It highlights the exceptional cases where the equality does not hold.

Abstract

Let $G=A_n$, a finite alternating group. We study the commuting graph of $G$ and establish, for all possible values of $n$ barring $13, 14, 17$ and $19$, whether or not the independence number is equal to the clique-covering number.