Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

Abstract

Let Γ be a graph and G⩽Aut(Γ). A graph Γ can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection p:Γ¯→Γ is arc-transitive (AT) if an AT subgroup of Aut(Γ) lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the C13 graph.