The Automorphism Groups of Arc-Transitive Abelian p-Covers of $$K_5$$ K 5

Abstract

In the classification of arc-transitive covering graphs, not many effective methods are known to determine the full automorphism groups of the covering graphs. The reason is that, for each automorphism of the covering graph, it is difficult to tell the projection along a given regular covering projection. In this paper, for eacharc-transitive abelian p-group covering graph of the complete graph $$K_5$$ where p is an odd prime, we investigate the size of each arc-transitive subgroup of automorphisms by determining the possibility of each vertex-stabiliser.