On Haar digraphical representations of groups

2020/01/12 by Du, Jia-Li, Feng, Yan-Quan, Spiga, Pablo
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.03914

Abstract

In this paper we extend the notion of digraphical regular representations in the context of Haar digraphs. Given a group G, a \em Haar digraph Γ over G is a bipartite digraph having a bipartition \X,Y\ such that G is a group of automorphisms of Γ acting regularly on X and on Y. We say that G admits a \em Haar digraphical representation (HDR for short), if there exists a Haar digraph over G such that its automorphism group is isomorphic to G. In this paper, we classify finite groups admitting a HDR.

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