$\omega$-Periodic Graphs

Itai Benjamini, Christopher Hoffman


$\omega$-Periodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree $\omega$-periodic graphs are amenable. We also provide examples of $\omega$-periodic graphs which have exponential volume growth, non-linear polynomial volume growth and intermediate volume growth.

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