Geometriae Dedicata

, Volume 5, Issue 1, pp 117-127

First online:

Automorphic graphs and the Krein condition

  • Norman BiggsAffiliated withRoyal Holloway College, University of London

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An automorphic graph is a distance-transitive graph, not a complete graph or a line graph, whose automorphism group acts primitively on the vertices. This paper shows that, for small values of the valency and diameter, such graphs are rare. The basic tool is the intersection array, for which there are several very restrictive feasibility conditions. In particular, a slight generalisation of the Krein condition of Scott and Higman is given, with a simplified proof.