This article is cited in 1 paper

RESEARCH ARTICLE

Some properties of various graphs associated with finite groups

X. Y. Chen^a, A. R. Moghaddamfar^b, M. Zohourattar<sup>b

a</sup> School of Sciences, Henan University of Technology, 450001, Zhengzhou, China
^b Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

Abstract: In this paper we investigate some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it is shown that the simple group $L_2(7)$ can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we obtain an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.

Keywords: power graph, commuting graph, tree-number, simple group.

MSC: 05C25, 20D05, 20D06

Received: 06.06.2018
Revised: 04.03.2019

Language: English

DOI: 10.12958/adm1197