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We consider the domino problem on Schreier graphs of self-similar groups, andmore generally their monadic second-order logic. On the one hand, we prove thatif the group is bounded then the graph's monadic second-order logic isdecidable. This covers, for example, the Sierpi\'nski gasket graphs and theSchreier graphs of the Basilica group. On the other hand, we already proveundecidability of the domino problem for a class of self-similar groups,answering a question by Barbieri and Sablik, and some examples including one oflinear growth.

Monadic second-order logic and the domino problem on self-similar graphs