Arc-transitive elementary abelian covers of the octahedron graph

Abstract

In this paper, we construct the pairwise non-congruent elementary abelian covers of the octahedron graph O-6 which admit a lift of an arc-transitive group of automorphisms of O-6. It shows that if the covering transformation group is a 2-group, then its rank is less than or equal to 7 and there exist exactly 14 non-congruent covering projections in total which admit lifts of arc-transitive subgroups of the full automorphism group of O-6. If the covering transformation group is an odd prime p-group, then its rank is 1, 3, 4, 6 or 7 and there exist p + 4 such non-congruent covering projections in total. (C) 2008 Elsevier Inc. All rights reserved.