Automorphism groups of graph covers and uniform subset graphs

Abstract

Hofmeister considered the automorphism groups of antipodal graphs through the exploration of graph covers. In this note weextend the exploration of automorphism groups of distance preserving graph covers. We apply the technique of graph covers todetermine the automorphism groups of uniform subset graphsΓ(2k,k,k−1) andΓ(2k,k,1).The determination of automorphismgroups answers a conjecture posed by Mark Ramras and Elizabeth Donovan. They conjectured that Aut(Γ(2k,k,k−1))∼=S2k×<T>,whereTis the complementation mapX↦→T(X)=Xc={1,2,...,2k}\X,andXis ak-subset ofΩ={1,2,...,2k}.