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

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.

18 pages

Cited by in corpus (1)

• Growth of Schreier graphs of automaton groups