On G-arc-regular dihedrants and regular dihedral maps

István Kovács, Dragan Marušič, Mikhail Muzychuk

Research output: Contribution to journalArticlepeer-review

15 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 languageEnglish
Pages (from-to)437-455
Number of pages19
JournalJournal of Algebraic Combinatorics
Volume38
Issue number2
DOIs
StatePublished - 1 Sep 2013
Externally publishedYes

Keywords

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

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