On dihedrants admitting arc-regular group actions
نویسندگان
چکیده
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 D2n ≤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 ⊗ · · · ⊗Kn )[Kc m], where 2n= n1 · · ·n m, and the numbers ni are pairwise coprime. Applications to 1-regular dihedrants and Cayley maps on dihedral groups are also given.
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