摘要

In this paper, we study arc-transitive graphs of order twice a prime power and any prime valency. In particular, we characterize such graphs which are 'basic' (admitting an arc-transitive automorphism group that has no intransitive normal subgroup such that the respective quotient graph retains the valence of the original graph). As an application, arc-transitive graphs of order twice a prime square and any prime valency are characterized, extending a few previous results.