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{\bf Itai Benjamini and Christopher Hoffman}
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{\bf $\omega$-Periodic Graphs}
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$\omega$-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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