The number of spanning trees of finite Sierpi´ nski graphs
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The proof proceeds in two steps: First, we show that the number of spanning trees and two further quantities satisfy a 3-dimensional polynomial recursion using the self-similar structure. Secondly, it turns out, that the dynamical behavior of the recursion is given by a 2-dimensional polynomial map, whose iterates can be computed explicitly.
[1] Martin T. Barlow,et al. Diffusions on fractals , 1998 .
[2] G. Kirchhoff. Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .
[3] J. Kigami,et al. Analysis on Fractals , 2001 .
[4] Stephan G. Wagner,et al. Enumeration problems for classes of self-similar graphs , 2007, J. Comb. Theory A.
[5] Tadashi Shima. On eigenvalue problems for the random walks on the Sierpinski pre-gaskets , 1991 .