Elementary abelian p-groups of rank 2p+3 are not CI-groups

Abstract

For every prime p>2 we exhibit a Cayley graph on $\mathbb{Z}_{p}^{2p+3}$ which is not a CI-graph. This proves that an elementary abelian p-group of rank greater than or equal to 2p+3 is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra. Moreover, we apply our technique to give a uniform explanation for the recent works of Muzychuk and Spiga concerning the problem.