Elementary abelian groups of rank 5 are DCI-groups

Abstract

In this paper, we show that the group ${\mathbb{Z}}_p^5$ is a DCI-group for any odd prime $p,$ that is, two Cayley digraphs Cay$({\mathbb{Z}}_p^5,S)$ and Cay$({\mathbb{Z}}_p^5,T)$ are isomorphic if and only if $S=T^{\phi }$ for some automorphism $\phi$ of the group ${\mathbb{Z}}_p^5$.