ON THE GENUS OF THE COMMUTING GRAPHS OF FINITE NON-ABELIAN GROUPS

Authors : Ashish Kumar Das, Deiborlang Nongsiang

Pages : 91-109

Doi:10.24330/ieja.266195

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Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :The commuting graph of a non-abelian group is a simple graph in which the vertices are the non-central elements of the group, and two distinct vertices are adjacent if and only if they commute. In this paper, we determine insert ignore into journalissuearticles values(up to isomorphism); all finite non-abelian groups whose commuting graphs are acyclic, planar or toroidal. We also derive explicit formulas for the genus of the commuting graphs of some well-known class of finite non-abelian groups, and show that, every collection of isomorphism classes of finite non-abelian groups whose commuting graphs have the same genus is finite.
Keywords : Commuting graph, finite group, AC group, genus of the commuting graphs