Spectrum and genus of commuting graphs of some classes of finite rings

Jutirekha Dutta; Walaa Nabil Taha Fasfous; Rajat Kanti Nath

doi:10.12697/ACUTM.2019.23.01

Jutirekha Dutta Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam
Walaa Nabil Taha Fasfous Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam
Rajat Kanti Nath Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam

DOI: https://doi.org/10.12697/ACUTM.2019.23.01

Keywords: integral graph, commuting graph, spectrum, genus

Abstract

We consider commuting graphs of some classes of finite rings and compute their spectrum and genus. We show that the commuting graph of a finite CC-ring is integral. We also characterize some finite rings whose commuting graphs are planar.

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