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arXiv · 2107.14279

On $n$-partite digraphical representations of finite groups

Jia-Li Du·Yan-Quan Feng·Pablo Spiga
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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.

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Jia-Li Du, Yan-Quan Feng, Pablo Spiga. 2021-07-29. On $n$-partite digraphical representations of finite groups. https://arxiv.org/abs/2107.14279

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