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Some Two-Point Resistances of the Sierpinski Gasket Network

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Abstract

In this paper, we use the principle of substitution to replace sub-gaskets of the Sierpinski gasket network by an equivalent Y-network which enables the use of only the Delta–Wye transformation and the series and parallel principles to derive some two-point resistances of the Sierpinski gasket network with dimension two.

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Acknowledgements

We are grateful to the referees for providing some helpful revising suggestions. Particularly, one of referees told us that \(R_{S(n)}(a_{n1} \cdot a_{n2})\) can be obtained by the results on the number of spanning trees in [22] and he (or she) also pointed out that \(R_{SG_d(n)}(a_{n1},a_{n2})\) can be obtained in a similar method.

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  1. School of Sciences, Jimei University, Xiamen, 361021, China

    Zhuozhuo Jiang & Weigen Yan

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  1. Zhuozhuo Jiang
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  2. Weigen Yan
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Correspondence to Weigen Yan.

Additional information

The author Weigen Yan was supported in part by NSFC Grants (11171134, 11571139).

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Jiang, Z., Yan, W. Some Two-Point Resistances of the Sierpinski Gasket Network. J Stat Phys 172, 824–832 (2018). https://doi.org/10.1007/s10955-018-2067-0

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