Weighted Spanning Trees on some Self-Similar Graphs
Daniele D’Angeli, Alfredo Donno · The Electronic Journal of Combinatorics · 2011
We compute the complexity of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński 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.