On dihedrants admitting arc-regular group actions
Dragan Marušič, Mikhail Muzychuk and István Kovács
J. algebr. comb. Volume 35, Number 3, pp. 409-426, 2011. ISSN 0925-9899

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 (Kn1Kn)[Kcm], where 2n=n 1⋅⋅⋅n ℓ m, and the numbers n i are pairwise coprime. Applications to 1-regular dihedrants and Cayley maps on dihedral groups are also given.

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