Arc-transitive elementary abelian covers of graphs

Boštjan Kuzman (University of Ljubljana)

Investigating the automorphism lifting problem in the context of elementary abelian covers, Malnič, Marušič and Potočnik derived a criterion describing $\alpha$-admissible covers in terms of $[\alpha]$-invariant subspaces for a certain matrix representation $[\alpha]$ of $\alpha\in{\rm Aut}(X)$. Their results have been succesfully applied in order to classify elementary abelian covers with specific symmetric properties for a number of small cubic or tetravalent graphs.  In this talk, I will present recent classification results for arc-transitive elementary abelian covers of $K_5$ and $K_{4,4}$.