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Resistance distances and the Kirchhoff index in double graphs

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Abstract

Let \(G\) be a connected graph, and let \(DG\) denote the double graph of \(G\). In this paper, we first derive closed-form formulas for resistance distances and the Kirchhoff index of \(DG\) in terms of that of \(G\). Then closed-form formulas for general \(k\)-iterated double graphs are also obtained. Finally, as illustration examples, for several special kinds of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for resistance distances and Kirchhoff indices of their \(k\)-iterated double graphs are given respectively.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (grant 11171134, 11301217) and the Natural Science Foundation of Fujian Province, China (grant 2011J01015, 2013J01014).

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, 361021, Fujian, People’s Republic of China

    Qinying Huang, Haiyan Chen & Qingying Deng

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  1. Qinying Huang
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  2. Haiyan Chen
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  3. Qingying Deng
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Correspondence to Haiyan Chen.

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Huang, Q., Chen, H. & Deng, Q. Resistance distances and the Kirchhoff index in double graphs. J. Appl. Math. Comput. 50, 1–14 (2016). https://doi.org/10.1007/s12190-014-0855-5

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  • DOI: https://doi.org/10.1007/s12190-014-0855-5

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