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Spectrum and genus of commuting graphs of some classes of finite rings. (English) Zbl 1428.16020

Summary: 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.

MSC:

16P10 Finite rings and finite-dimensional associative algebras
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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