Abstract

A finite non-abelian group $G$ is called commuting integral if the commuting graph of $G$ is integral. In this paper, we show that a finite group is commuting integral if its central 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 $2m$.

Keywords: Integral graph; commuting graph; spectrum of a graph.

MSC: 05C25, 05C50, 20D60

Pages:  226--230     

Volume  69 ,  Issue  3 ,  2017