Infinite distance transitive graphs of finite valency


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.

This is a preview of subscription content, access via your institution.


  1. [1]

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

    Google Scholar 

  2. [2]

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

    MATH  MathSciNet  Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Macpherson, H.D. Infinite distance transitive graphs of finite valency. Combinatorica 2, 63–69 (1982).

Download citation

AMS subject classification (1980)

  • 05 C 25