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

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.

transitive graph, quasiisometry, growth rate, number of ends, asymptotic dimension
Mathematical Subject Classification
Primary: 20F18, 20F65, 20F69, 51F30
Received: 1 October 2021
Revised: 22 February 2022
Accepted: 26 February 2022
Published: 14 July 2022
Josiah Oh
The Ohio State University
Columbus, OH
United States
Mark Pengitore
University of Virginia
Charlottesville, VA
United States