On dihedrants admitting arc-regular group actions

István Kovács, Dragan Marušič, Mikhail E. Muzychuk

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10 Scopus citations

Abstract

We consider Cayley graphs Γ over dihedral groups, dihedrants for short, which admit an automorphism group G acting regularly on the arc set of Γ. We prove that, if D 2n ≤ G≤ Aut(Γ) is a regular dihedral subgroup of G of order 2n such that any of its index 2 cyclic subgroups is core-free in G, then Γ belongs to the family of graphs of the form (Kn1⊗⋯⊗ Knl)[Km c], where 2n=n 1⋯nlm, and the numbers n i are pairwise coprime. Applications to 1-regular dihedrants and Cayley maps on dihedral groups are also given.

Original languageEnglish
Pages (from-to)409-426
Number of pages18
JournalJournal of Algebraic Combinatorics
Volume33
Issue number3
DOIs
StatePublished - 1 May 2011
Externally publishedYes

Keywords

  • Arc-transitive graph
  • Cayley graph
  • Cayley map
  • Core-free group
  • Dihedral group

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