On n-partite digraphical representations of finite groups

A group G admits an n-partite digraphical representation if there exists a regular n-partite digraph gamma such that the automorphism group Aut(gamma;) of gamma satisfies the following properties:& nbsp;(1) Aut(gamma) is isomorphic to G,& nbsp;(2) Aut(gamma) acts semiregularly on the vertices of gamma and & nbsp;(3) the orbits of Aut(gamma) on the vertex set of gamma form a partition into n parts giving a structure of n-partite digraph to gamma.& nbsp;In this paper, for every positive integer n, we classify the finite groups admitting an n-partite digraphical representation. (C)& nbsp;2022 Elsevier Inc. All rights reserved.