On a family of Schreier graphs of intermediate growth associated with a self-similar group
نویسندگان
چکیده
For every infinite sequence ω = x1x2 . . ., with xi ∈ {0, 1}, we construct an infinite 4-regular graph Xω. 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 Xω have intermediate growth.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 33 شماره
صفحات -
تاریخ انتشار 2012