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Mathematics > Group Theory

arXiv:1806.02102 (math)
[Submitted on 6 Jun 2018]

Title:Some properties of various graphs associated with finite groups

Authors:Xiaoyou Chen, Alireza Moghaddamfar, Mahsa Zohourattar
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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 $L_2(7)$ can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we have obtained an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.
Comments: 13 pages
Subjects: Group Theory (math.GR)
MSC classes: 05C25, 20D05, 20D06
Cite as: arXiv:1806.02102 [math.GR]
  (or arXiv:1806.02102v1 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1806.02102

Submission history

From: Alireza Moghaddamfar - [view email]
[v1] Wed, 6 Jun 2018 10:33:38 UTC (12 KB)
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