Some properties of various graphs associated with finite groups

2018/06/06 by Chen, Xiaoyou, Moghaddamfar, Alireza, Zohourattar, Mahsa
#05C25 #20D05 #20D06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1806.02102

Abstract

In this paper we have investigated some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it has been shown that the simple group L₂(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 have obtained an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.

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