Genus of commuting graphs of some classes of finite rings

Abstract

In this paper, we compute the genus of commuting graphs of non-commutative rings of order $p^4$, $p^5$, $p^{2}q$ and $p^{3}q$, where $p$ and $q$ are prime integers. We also characterize those finite rings such that their commuting graphs are planar or toroidal.

9 pages