On Quotientable Arc-transitive Graphs

We call an arc-transitive graph Gamma quotientable if it is a regular covering graph of an arc-transitive simple graph, and otherwise, Gamma is basic. In this paper, we investigate the quotientability of cubic arc-transitive graphs. It is proved that for any prime p > 3, a cubic arc-transitive graph of order 2p(2) is quotientable if and only if p equivalent to 1 mod 3. In addition, we prove that besides several special families, every cubic arc-transitive graph with arc-transitive solvable automorphism subgroups is quotientable. Moreover, two infinite families of quotientable cubic arc-transitive graphs, which are regular but non normal covering graphs, are given.