On n-partite digraphical representations of finite groups

2021/07/29 by Du, Jia-Li, Feng, Yan-Quan, Spiga, Pablo
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2107.14279

Abstract

A group G admits an \em n-partite digraphical representation if there exists a regular n-partite digraph Γ such that the automorphism group Aut(Γ) of Γ satisfies the following properties: Aut(Γ) is isomorphic to G, Aut(Γ) acts semiregularly on the vertices of Γ and the orbits of Aut(Γ) on the vertex set of Γ form a partition into n parts giving a structure of n-partite digraph to Γ. In this paper, for every positive integer n, we classify the finite groups admitting an n-partite digraphical representation.

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