This paper studies whether there are distance-transitive graphs arising from the coset actions of G2(q) on the subfield subgroup G2( √ q) or G2(q) on the Ree subgroup 2G2(q). It is found that there are no such graphs, even if the groups are extended by outer automorphisms of G2(q).

We present a new result on distance-transitive graphs and show how it can be used in the case where the vertex stabilizer is the centralizer of some involution.

IntroductionThis paper represents the first step in the classification of finite primitive distancetransitive graphs. In it we reduce the problem to the case where the automorph-ism group is either… Expand

A permutation representation of a finite group is multiplicity-free if all the irreducible constituents in the permutation character are distinct. There are three main reasons why these… Expand