Combinatorica

, Volume 2, Issue 1, pp 63–69

Infinite distance transitive graphs of finite valency

  • H. D. Macpherson
Article

Abstract

We determine all infinite distance transitive graphs of finite valency, thereby proving a conjecture of C. D. Godsil. The proof makes heavy use of a theorem of M. J. Dunwoody concerning cuts of infinite graphs. In section 1 there is a rough analysis of the appearance of such graphs, and in section 2 we state and apply Dunwoody’s theorem. The proof is completed in section 3.

AMS subject classification (1980)

05 C 25 

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References

  1. [1]
    N. L. Biggs,Algebraic graph theory, Cambridge University Press, Cambridge, (1974).MATHGoogle Scholar
  2. [2]
    M. J. Dunwoody, Cutting up graphs,Combinatorica 2 (1) (1982), 15–23.MATHMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1982

Authors and Affiliations

  • H. D. Macpherson
    • 1
  1. 1.Merton CollegeOxfordEngland

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