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Spanning Trees on the Sierpinski Gasket

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Abstract

We present the numbers of spanning trees on the Sierpinski gasket SG d (n) at stage n with dimension d equal to two, three and four. The general expression for the number of spanning trees on SG d (n) with arbitrary d is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket SG d,b (n) with d = 2 and b = 3,4 are also obtained.

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Authors and Affiliations

  1. Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan

    Shu-Chiuan Chang

  2. Physics Division, National Center for Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan

    Shu-Chiuan Chang

  3. Department of Mathematics, Fu Jen Catholic University, Taipei, 24205, Taiwan

    Lung-Chi Chen

  4. Department of Mathematics, Temple University, Philadelphia, PA, 19122, USA

    Wei-Shih Yang

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  1. Shu-Chiuan Chang
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  2. Lung-Chi Chen
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  3. Wei-Shih Yang
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Correspondence to Shu-Chiuan Chang.

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Chang, SC., Chen, LC. & Yang, WS. Spanning Trees on the Sierpinski Gasket. J Stat Phys 126, 649–667 (2007). https://doi.org/10.1007/s10955-006-9262-0

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