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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
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.
Received: 06.06.2018 Revised: 04.03.2019
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
Linking options:
https://www.mathnet.ru/eng/adm795 https://www.mathnet.ru/eng/adm/v31/i2/p195
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Abstract page: | 44 | Full-text PDF : | 45 | References: | 23 |
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