On quotientable arc-transitive graphs

Abstract

We call an arc-transitive graph Γ quotientable if it is a regular covering graph of an arc-transitive simple graph, and otherwise, Γ 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 2p2 is quotientable if and only if p = 1 mod 3. In addition, we prove that besides several special families, every cubic arc-transitive graph with arc-transitive solvable automor-phism subgroups is quotientable. Moreover, two infinite families of quotientable cubic arc-transitive graphs, which are regular but non-normal covering graphs, are given. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.