Distance Sequences of Locally Infinite Primitive Graphs

Abstract

A graph is called primitive if its automorphism group acts primitively on the vertex set. In this paper, we prove a classification of the possible distance sequences of locally infinite primitive graphs. In particular we show that if a primitive graph is locally uncountable, the distance sequence is constant until it terminates. We also prove a constraint on the distance sequences of locally finite infinite graphs.

7 pages, 2 figures