Infinite distance transitive graphs of finite valency

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.

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References

  1. [1]

    N. L. Biggs,Algebraic graph theory, Cambridge University Press, Cambridge, (1974).

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  2. [2]

    M. J. Dunwoody, Cutting up graphs,Combinatorica 2 (1) (1982), 15–23.

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Macpherson, H.D. Infinite distance transitive graphs of finite valency. Combinatorica 2, 63–69 (1982). https://doi.org/10.1007/BF02579282

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AMS subject classification (1980)

  • 05 C 25