On a family of Schreier graphs of intermediate growth associated with a self-similar group
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abstract
For every infinite sequence =x 1 x 2 ..., with x i {0, 1}, we construct an infinite 4-regular graph X . 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 have intermediate growth. 2012 Elsevier Ltd.