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On a family of Schreier graphs of intermediate growth associated with a self-similar group (1106.3979v1)
Published 20 Jun 2011 in math.GR and math.CO
Abstract: For every infinite sequence $\omega=x_1,x_2,...$, with $x_i\in{0,1}$, we construct an infinite 4-regular graph $X_{\omega}$. 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 $X_\omega$ have intermediate growth.