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arXiv · 1604.07133

Spectrum of commuting graphs of some classes of finite groups

Jutirekha Dutta·Rajat Kanti Nath
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Abstract

In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups. We show that the commuting graphs of finite non-abelian AC-groups are integral. We also show that the commuting graph of a finite non-abelian group $G$ is integral if $G$ is not isomorphic to the symmetric group of degree $4$ and the commuting graph of $G$ is planar. Further it is shown that the commuting graph of $G$ is integral if the commuting graph of $G$ is toroidal.

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Jutirekha Dutta, Rajat Kanti Nath. 2016-04-25. Spectrum of commuting graphs of some classes of finite groups. https://arxiv.org/abs/1604.07133

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