CI-property of $C_p^2 \times C_n$ and $C_p^2 \times C_q^2$ for digraphs

TL;DR

This paper establishes that certain direct products of elementary abelian groups and cyclic groups are DCI-groups, extending previous results and contributing to the understanding of symmetry properties in algebraic structures.

Contribution

It proves that specific direct products of elementary abelian and cyclic groups are DCI-groups, generalizing earlier findings on cyclic groups.

Findings

Direct product of two coprime elementary abelian groups of rank two are DCI-groups.

Direct product of a cyclic prime order group and a square-free order cyclic group are DCI-groups.

Extension of Muzychuk's result on cyclic groups to broader classes of groups.

Abstract

We prove that the direct product of two coprime order elementary abelian groups of rank two, as well as the direct product of a cyclic group of prime order and a cyclic group of square free order are DCI-groups. The latter is a generalization of Muzychuk's result on cyclic groups (J. Combin. Theory Ser. A, 1995).