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On n-partite digraphical representations of finite groups
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2022-02-23 , DOI: 10.1016/j.jcta.2022.105606
Jia-Li Du 1 , Yan-Quan Feng 2 , Pablo Spiga 3
Affiliation  

A group G admits an 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:

(1)

Aut(Γ) is isomorphic to G,

(2)

Aut(Γ) acts semiregularly on the vertices of Γ and

(3)

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.



中文翻译:

关于有限群的 n 部对数表示

如果存在正则n部有向图 Γ 使得自同构群,则群G承认n 部有向图表示自动(Γ)Γ 满足以下性质:

(1)

自动(Γ)与G同构,

(2)

自动(Γ)半规则地作用于 Γ 和

(3)

的轨道自动(Γ)在 Γ 的顶点集上形成一个划分为n 个部分,给Γ 一个n部分有向图的结构。

在本文中,对于每个正整数n,我们对允许n部图表示的有限群进行分类。

更新日期:2022-02-23
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