Geometriae Dedicata

, Volume 5, Issue 1, pp 117–127

Automorphic graphs and the Krein condition

Authors

  • Norman Biggs
    • Royal Holloway CollegeUniversity of London
Article

DOI: 10.1007/BF00148146

Cite this article as:
Biggs, N. Geom Dedicata (1976) 5: 117. doi:10.1007/BF00148146

Abstract

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.

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Copyright information

© D. Reidel Publishing Company 1976