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Algebra and Discrete Mathematics, 2021, Volume 31, Issue 2, Pages 195–211
DOI: https://doi.org/10.12958/adm1197 (Mi adm795) 		 
RESEARCH ARTICLE

Some properties of various graphs associated with finite groups

X. Y. Chena, A. R. Moghaddamfarb, M. Zohourattarb

a 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
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DOI: https://doi.org/10.12958/adm1197
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.
Funding agency Grant number
Henan University of Technology
Project of Henan Province 182102410049
Natural Science Foundation of China 11926330
11926326
11971189
11771356
The first author thanks Cultivation Programme for Young Backbone Teachers in Henan University of Technology, the Project of Henan Province (182102410049), and NSFC (11926330, 11926326, 11971189, 11771356).
Received: 06.06.2018
Revised: 04.03.2019
Document Type: Article
MSC: 05C25, 20D05, 20D06
Language: English
Citation: X. Y. Chen, A. R. Moghaddamfar, M. Zohourattar, “Some properties of various graphs associated with finite groups”, Algebra Discrete Math., 31:2 (2021), 195–211
Citation in format AMSBIB
\Bibitem{CheMogZoh21}
\by X.~Y.~Chen, A.~R.~Moghaddamfar, M.~Zohourattar
\paper Some properties of various graphs associated with finite groups
\jour Algebra Discrete Math.
\yr 2021
\vol 31
\issue 2
\pages 195--211
\mathnet{http://mi.mathnet.ru/adm795}
\crossref{https://doi.org/10.12958/adm1197}
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