Combinatorica

, Volume 26, Issue 5, pp 577–585 | Cite as

Distance Sequences In Locally Infinite Vertex-Transitive Digraphs

Original Paper

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 vertex-transitive undirected graph of infinite degree d, we have f(k)=d for all k, 1≤k<diam(G). This answers a question by L. Babai.

Mathematics Subject Classification (2000):

05C12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityPiscataway, NJUSA

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