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On Haar digraphical representations of groups. (English) Zbl 07233255

Summary: In this paper we extend the notion of digraphical regular representations in the context of Haar digraphs. Given a group \(G\), a Haar digraph \(\Gamma\) over \(G\) is a bipartite digraph having a bipartition \(\{ X , Y \}\) such that \(G\) is a group of automorphisms of \(\Gamma\) acting regularly on \(X\) and on \(Y\). We say that \(G\) admits a 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 an HDR.

MSC:

05E18 Group actions on combinatorial structures
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures

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References:

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