Geometry of nontransitive graphs

Josiah Oh and Mark Pengitore

Vol. 317 (2022), No. 2, 423–440

DOI: 10.2140/pjm.2022.317.423

Abstract

We study nontransitive graphs and prove a number of results when they satisfy a coarse version of transitivity. Also, for each finitely generated group $G$, we produce continuum many pairwise non-quasiisometric regular graphs that have the same growth rate, number of ends, and asymptotic dimension as $G$.

Keywords

transitive graph, quasiisometry, growth rate, number of ends, asymptotic dimension

Mathematical Subject Classification

Primary: 20F18, 20F65, 20F69, 51F30

Milestones

Received: 1 October 2021

Revised: 22 February 2022

Accepted: 26 February 2022

Published: 14 July 2022