On $n$-partite digraphical representations of finite groups

DOI10.1016/J.JCTA.2022.105606arXiv2107.14279MaRDI QIDQ6374098

Yan-Quan Feng, Jia-Li Du, Pablo Spiga

Publication date: 29 July 2021

Abstract: A group $G$ admits an extbf{em $n$-partite digraphical representation} if there exists a regular $n$-partite digraph $Gamma$ such that the automorphism group $mathrmAut(Gamma)$ of $Gamma$ satisfies the following properties: $mathrmAut(Gamma)$ is isomorphic to $G$, $mathrmAut(Gamma)$ acts semiregularly on the vertices of $Gamma$ and the orbits of $mathrmAut(Gamma)$ 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.

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Representation theory of groups (20C99) Directed graphs (digraphs), tournaments (05C20) Group actions on combinatorial structures (05E18)

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