Spectrum of commuting graphs of some classes of finite groups

Authors

  • Rajat Kanti Nath Tezpur UNiversity
  • Jutirekha Dutta Tezpur University

DOI:

https://doi.org/10.11113/matematika.v33.n1.812

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 its commuting graph is toroidal.

Author Biographies

Rajat Kanti Nath, Tezpur UNiversity

Department of Mathematical Sciences, Assistant Professor

Jutirekha Dutta, Tezpur University

Department of Mathematical Sciences, Research Scholar

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Published

2017-09-20

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Section

Articles