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arXiv · 1106.3979

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

Ievgen Bondarenko·Tullio Ceccherini-Silberstein·Alfredo Donno·Volodymyr Nekrashevych
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Abstract

For every infinite sequence $ω=x_1,x_2,...$, with $x_i\in\{0,1\}$, 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 $\{0,1\}^{\infty}$. 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.

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Ievgen Bondarenko, Tullio Ceccherini-Silberstein, Alfredo Donno, Volodymyr Nekrashevych. 2011-06-20. On a family of Schreier graphs of intermediate growth associated with a self-similar group. https://arxiv.org/abs/1106.3979

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