, Volume 2, Issue 1, pp 63-69

Infinite distance transitive graphs of finite valency

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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.