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

The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two vertices $x,y$ are adjacent if and only if $xy=yx$. In this paper, we compute the spectrum and genus of commuting graphs of some classes of finite rings.