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Combinatorica

, Volume 8, Issue 4, pp 333–343 | Cite as

Bounding the diameter of distance-regular graphs

  • C. D. Godsil
Article

Abstract

LetG be a connected distance-regular graph with valencyk>2 and diameterd, but not a complete multipartite graph. Suppose thatθ is an eigenvalue ofG with multiplicitym and thatθ≠±k. We prove that bothd andk are bounded by functions ofm. This implies that, ifm>1 is given, there are only finitely many connected, co-connected distance-regular graphs with an eigenvalue of multiplicitym.

AMS subject classification code (1980)

05 C 99 

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Copyright information

© Akadémiai Kiadó 1988

Authors and Affiliations

  • C. D. Godsil
    • 1
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

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