On the genus of the commuting graphs of finite non-abelian groups

Ashish Kumar Das; Deiborlang Nongsiang

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arXiv · 1311.6342

On the genus of the commuting graphs of finite non-abelian groups

Ashish Kumar Das·Deiborlang Nongsiang

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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 classify (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 finite non-abelian groups whose commuting graphs have the same genus is finite.

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BibTeX RIS

Ashish Kumar Das, Deiborlang Nongsiang. 2013-11-25. On the genus of the commuting graphs of finite non-abelian groups. https://arxiv.org/abs/1311.6342

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