On $n$-partite digraphical representations of finite groups

Abstract

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

9 pages

References in corpus (1)

• Every finite non-solvable group admits an Oriented Regular Representation