On a family of Schreier graphs of intermediate growth associated with a self-similar group

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Abstract

For every infinite sequence ω=x 1 x 2 ..., with x i ∈{0, 1}, we construct an infinite 4-regular graph X ω . These graphs are precisely the Schreier graphs of the action of a certain self-similar group on the space {0, 1} ∞ . We solve the isomorphism and local isomorphism problems for these graphs, and determine their automorphism groups. Finally, we prove that all graphs X ω have intermediate growth. © 2012 Elsevier Ltd.

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APA

Bondarenko, I., Ceccherini-Silberstein, T., Donno, A., & Nekrashevych, V. (2012). On a family of Schreier graphs of intermediate growth associated with a self-similar group. European Journal of Combinatorics, 33(7), 1408–1421. https://doi.org/10.1016/j.ejc.2012.03.006

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