A classification of the graphical m-semiregular representation of finite groups

Du, Jian; Yan, Feng; Spiga, Pablo

doi:10.1016/j.jcta.2019.105174

Cited by 9 publications

(4 citation statements)

References 28 publications

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“…Observe that every n-PDR is also a DnSR, but not every DnSR is necessarily a n-PDR because it may not be n-partite. Therefore, Theorem 1.1 can be seen as an extension of the classification in [8] of the finite groups admitting a DnSR. The second generalisation we discuss is concerned with Haar digraphs.…”

Section: Introductionmentioning

confidence: 98%

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On Haar digraphical representations of groups

Yan

Spiga

2020

Discrete Mathematics

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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.

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Section: Introductionmentioning

confidence: 98%

“…Morris and Spiga [13,14,15], answering a question of Babai [1], classified the finite groups admitting an oriented regular representation. For more results, generalising DRRs in various directions, we refer to [7,8,9,12,16,18]. To give some more context to Theorem 1.1, we give details to two more particular generalisations.…”

Section: Introductionmentioning

confidence: 99%

On Haar digraphical representations of groups

Yan

Spiga

2020

Discrete Mathematics

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“…Morris and Spiga [18,19,22], answering a question of Babai [2], have classified the finite groups admitting an oriented regular representation, ORR for short. For more results, generalising the classical DRR and GRR classification in various direction, we refer to [5,7,6,17,23,24,26].…”

Section: Introductionmentioning

confidence: 99%

“…We say that a group G admits a (di)graphical m-semiregular representation (DmSR and GmSR, for short), if there exists a regular m-Cayley (di)graph Γ over G such that Aut(Γ) ∼ = G. In particular, D1SRs and G1SRs are the usual GRRs and DRRs. For each m ∈ N, we have classified in [6] the finite groups admitting a DmSR and the finite groups admitting a GmSR. In this paper we propose a natural variant of this problem.…”

Section: Introductionmentioning

confidence: 99%

On Haar digraphical representations of groups

Yan

Spiga

2020

Preprint

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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 a HDR.

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On oriented m $m$‐semiregular representations of finite groups

Du,

Feng,

Bang

2024

Journal of Graph Theory

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A finite group admits an oriented regular representation if there exists a Cayley digraph of such that it has no digons and its automorphism group is isomorphic to . Let be a positive integer. In this paper, we extend the notion of oriented regular representations to oriented ‐semiregular representations using ‐Cayley digraphs. Given a finite group , an ‐Cayley digraph of is a digraph that has a group of automorphisms isomorphic to acting semiregularly on the vertex set with orbits. We say that a finite group admits an oriented ‐semiregular representation (OSR for short) if there exists an ‐Cayley digraph of such that it has no digons and is isomorphic to its automorphism group. Moreover, if is regular, that is, each vertex has the same in‐ and out‐valency, we say is a regular oriented ‐semiregular representation (regular OSR for short) of . In this paper, we classify finite groups admitting a regular OSR or an OSR for each positive integer .

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A classification of the graphical m-semiregular representation of finite groups

Cited by 9 publications

References 28 publications

On Haar digraphical representations of groups

On Haar digraphical representations of groups

On Haar digraphical representations of groups

On oriented m $m$‐semiregular representations of finite groups

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