Distance Sequences In Locally Infinite Vertex-Transitive Digraphs

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 by L. Babai.

• Type: Journal
• Year: 2006
• Where: COMBINATORICA
• Authors: Wesley Pegden
• Keywords: COMBINATORICA 2006, Infinite Degree, Out-distance Sequence, Vertex-transitive Digraph