Distance-transitive graphs

In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite simple groups, it seems possible to find all distance-transitive graphs. Priority is given to the classification of the so-called primitive ones. We give all account of the achievements in this direction