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Resistance distance local rules

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Abstract

In [D.J. Klein, Croat. Chem. Acta. 75(2), 633 (2002)] Klein established a number of sum rules to compute the resistance distance of an arbitrary graph, especially he gave a specific set of local sum rules that determined all resistance distances of a graph (saying the set of local sum rules is complete). Inspired by this result, we give another complete set of local rules, which is simple and also efficient, especially for distance-regular graphs. Finally some applications to chemical graphs (for example the Platonic solids as well as their vertex truncations, which include the graph of Buckminsterfullerene and the graph of boron nitride hetero-fullerenoid B 12 N 12) are made to illustrate our approach.

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Authors and Affiliations

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

    Haiyan Chen

  2. Institute of Mathematics, Xiamen University, 361005, Xiamen, China

    Fuji Zhang

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  1. Haiyan Chen
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  2. Fuji Zhang
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Correspondence to Haiyan Chen.

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Chen, H., Zhang, F. Resistance distance local rules. J Math Chem 44, 405–417 (2008). https://doi.org/10.1007/s10910-007-9317-8

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  • DOI: https://doi.org/10.1007/s10910-007-9317-8

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