Vol. 317, No. 2, 2022
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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.

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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
Authors
Josiah Oh
The Ohio State University
Columbus, OH
United States
Mark Pengitore
University of Virginia
Charlottesville, VA
United States