Arc-transitive Dihedrants of Odd Prime-power Order

Abstract

Let G be a finite group with identity element 1, and S be a subset of G such that $${1 \notin S}$$ and S = S ?1. The Cayley graph Cay(G, S) has vertex set G, and x, y in G are adjacent if and only if $${xy^{-1} \in S}$$ . In this paper we classify the connected, arc-transitive Cayley graphs $${{\rm Cay}(D_{2p^n}, S),}$$ where $${D_{2p^n}}$$ is the dihedral group of order 2p n , p is an odd prime.