Spanning forests on the Sierpinski gasket

Abstract

We present the numbers of spanning forests on the Sierpinski gasket $S{G}_d(n)$ at stage $n$ with dimension $d$ equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket $S{G}_{d,b}(n)$ with $d=2$ and $b=3,4$ are obtained. We also derive the upper bounds of the asymptotic growth constants for both $S{G}_d$ and $S{G}_{2,b}$.

31 pages, 9 figures, 7 tables

References in corpus (2)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Spanning trees on the Sierpinski gasket