We compute the complexity of two infinite families of finite graphs: the
Sierpi\'{n}ski graphs, which are finite approximations of the well-known
Sierpi\'nsky gasket, and the Schreier graphs of the Hanoi Towers group
H(3) acting on the rooted ternary tree. For both of them, we study the
weighted generating functions of the spanning trees, associated with several
natural labellings of the edge sets.Comment: 21 page