On Haar digraphical representations of groups
JL Du, YQ Feng, P Spiga - Discrete Mathematics, 2020 - Elsevier
JL Du, YQ Feng, P Spiga
Discrete Mathematics, 2020•ElsevierIn 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.
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.
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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