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Distance Sequences In Locally Infinite Vertex-Transitive Digraphs

2006
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Combinatorica
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We prove that the out-distance sequence {f + (k)} of a vertex-transitive digraph of finite or infinite degree satisfies f + (k + 1) ≤ f + (k) 2 for k ≥ 1, where f + (k) denotes the number of vertices at directed distance k from a given vertex. As a corollary, we prove that for a connected vertextransitive undirected graph of infinite degree d, we have f (k) = d for all k, 1 ≤ k < diam(G). This answers a question

doi:10.1007/s00493-006-0033-y
fatcat:xckh6n2ezzbqjlv67ctmplzism