On the Classification of Arc-transitive Circulant Digraphs of Order Odd-Prime-Squared

A Cayley graph Γ=Cay(G,S)of a group G with respect to S is called a circulant digraphof order p~k if G is a cyclic group of the same order.Investigated in this paper are the normalityconditions for arc-transitive circulant(all)graphs of order p~2 and the classification of all such graphs.Itis proved that any connected arc-transitive circulant digraph of order p~2 is,up to a graph isomorphism,either K~2,G(p~2,r),or G(p,r)[pK],where r|p-1.