On Distance-transitive Graphs
نویسنده
چکیده
Cameron's proof of this result is based on Sims' Conjecture, which has only been shown to hold using the classification of finite simple groups. In the final section of [1], Cameron indicates how Theorem 1 might be proved in an elementary fashion using Macpherson's classification of infinite distance-transitive graphs of finite valency [4]. Corollary 1 below provides the missing portion of this elementary proof. In fact, using in place of [4] a result of A. A. Ivanov, which yields the classification of infinite distance-regular graphs of finite valency as a corollary, we obtain a proof of Theorem 1 which also avoids the use of the Compactness Theorem suggested by Cameron. We first state the result of Ivanov [3]:
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