On G-arc-regular dihedrants and regular dihedral maps

István Kovács; Dragan Marušič; Mikhail Muzychuk

doi:10.1007/s10801-012-0410-0

On G-arc-regular dihedrants and regular dihedral maps

István Kovács, Dragan Marušič, Mikhail Muzychuk

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A graph Γ is said to be G-arc-regular if a subgroup G ≤ Aut(Γ) acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D _2n of order 2n whose cyclic subgroup C _n ≤D _2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D _2n, n odd, are classified.

Original language	English
Pages (from-to)	437-455
Number of pages	19
Journal	Journal of Algebraic Combinatorics
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/s10801-012-0410-0
State	Published - 1 Sep 2013
Externally published	Yes

Keywords

Cayley graph
Cayley map
Dihedral group
G-arc-regular graph

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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10.1007/s10801-012-0410-0

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title = "On G-arc-regular dihedrants and regular dihedral maps",

abstract = "A graph Γ is said to be G-arc-regular if a subgroup G ≤ Aut(Γ) acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D 2n of order 2n whose cyclic subgroup C n ≤D 2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D 2n, n odd, are classified.",

keywords = "Cayley graph, Cayley map, Dihedral group, G-arc-regular graph",

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AU - Kovács, István

AU - Marušič, Dragan

AU - Muzychuk, Mikhail

PY - 2013/9/1

Y1 - 2013/9/1

N2 - A graph Γ is said to be G-arc-regular if a subgroup G ≤ Aut(Γ) acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D 2n of order 2n whose cyclic subgroup C n ≤D 2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D 2n, n odd, are classified.

AB - A graph Γ is said to be G-arc-regular if a subgroup G ≤ Aut(Γ) acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D 2n of order 2n whose cyclic subgroup C n ≤D 2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D 2n, n odd, are classified.

KW - Cayley graph

KW - Cayley map

KW - Dihedral group

KW - G-arc-regular graph

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U2 - 10.1007/s10801-012-0410-0

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IS - 2

ER -

On G-arc-regular dihedrants and regular dihedral maps

Abstract

Keywords

ASJC Scopus subject areas

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