Some properties of various graphs associated with finite groups

X. Y. Chen, A. R. Moghaddamfar, M. Zohourattar


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.


power graph, commuting graph, tree-number, simple group

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