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.
|Title of host publication||Topics in Algebraic Graph Theory|
|Editors||L.W. Beineke, R.J. Wilson, P.J. Cameron|
|Place of Publication||Cambridge|
|Publisher||Cambridge University Press|
|Number of pages||290|
|Publication status||Published - 2004|
|Name||Encyclopedia of Mathematics and its Applications|