#### 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
##### 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