Finite groups whose commuting graphs are integral

Abstract

A finite non-abelian group $G$ is called commutingintegral if the commuting graph of $G$ is integral. In thispaper, we show that a finite group is commuting integral if itscentral quotient is isomorphic to ${\mathbb{Z}}_p\times {\mathbb{Z}}_p$ or $D_{2m}$, where $p$ is any prime integer and$D_{2m}$ is the dihedral group of order $2m$.