In this paper we extend the notion of digraphical regular representations in the context of Haar digraphs. Given a group G, a 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 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.
Du, J., Feng, Y., Spiga, P. (2020). On Haar digraphical representations of groups. DISCRETE MATHEMATICS, 343(10) [10.1016/j.disc.2020.112032].
On Haar digraphical representations of groups
Spiga P.
2020
Abstract
In this paper we extend the notion of digraphical regular representations in the context of Haar digraphs. Given a group G, a 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 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.
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