Finite groups whose commuting graphs are integral

J. Dutta and R. K. Nath

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.

Classification (MSC2000): 05C25; 05C50, 20D60

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