Non-commuting graph of AC-groups: as matroids
Group Theory
2025-05-20 v1
Abstract
Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph {\Gamma}G (called non-commuting graph of G) as follows: Take G\Z(G) as the vertices of {\Gamma}G and join x and y, whenever . In this paper, we show that a finite group G is an AC-group, if and only if, the associated non-commuting graph of G is a matroid. Leveraging the properties of matroids, we further delve into the characteristics of AC-groups. Additionally, we provide a formula to compute the clique number of the non-commuting graph of AC-groups, offering a new perspective on the structure of these groups
Cite
@article{arxiv.2505.12070,
title = {Non-commuting graph of AC-groups: as matroids},
author = {Azizollah Azad and Nasim Karimi and Sakineh Rahbariyan},
journal= {arXiv preprint arXiv:2505.12070},
year = {2025}
}