Affine distance-transitive graphs and exceptional Chevalley groups. (Q2766409)

This is an interesting but complex paper concerning the structure of graphs with distance transitive automorphism groups. One class of examples leads to the situation where the vertices of the graph can be considered as the points of a vector space \(V\) over a finite field, the automorphism group is the split extension of \(V\) by the stabilizer of \(0\), \(G_0\).NEWLINENEWLINE The authors consider the case where the action is primitive and the generalized Fitting subgroup is a central extension of an exceptional Chevalley group. In this case they show that the Chevalley group has to be \(E_6\), \(V\) is \(27\)-dimensional and they describe the graph.