Geodesic
Some properties of various graphs associated with finite groups
Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 195-211.

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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
Mots-clés : simple group. 
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X. Y. Chen; A. R. Moghaddamfar; M. Zohourattar. Some properties of various graphs associated with finite groups. Algebra and discrete mathematics, Tome 31 (2021) no. 2, pp. 195-211. http://geodesic.mathdoc.fr/item/ADM_2021_31_2_a1/

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