Mathematical logic, algebra and number theory

Groups with symmetric non-commuting graphs

A. Abdollahi

Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746-73441, Iran

Abstract: In this paper we characterize non-abelian finite $2$-generator groups $G$ whose non-commuting graphs are $\mathrm{Aut}(G)$-symmetric. We also find some general results on these groups. These partially answer Problem 31 posed in Peter Cameron's home page, old problems.

Keywords: non-commuting graph, automorphism group, symmetric graphs.

UDC: 512.54,519.17

MSC: 20D60, 05C25

Received June 24, 2021, published September 28, 2024

Language: English

DOI: 10.33048/semi.2024.21.044