Spanning trees on the Sierpinski gasket

Abstract

We obtain the numbers of spanning trees on the Sierpinski gasket $S{G}_d(n)$ with dimension $d$ equal to two, three and four. The general expression for the number of spanning trees on $S{G}_d(n)$ with arbitrary $d$ is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket $S{G}_{d,b}(n)$ with $d=2$ and $b=3,4$ are also obtained.

20 pages, 8 figures, 1 table

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