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Kemeny’s constant and the Kirchhoff index for the cluster of highly symmetric graphs

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  • Palacios, José Luis
  • Markowsky, Greg

Abstract

We find closed form formulas for the Kemeny’s constant and the Kirchhoff index for the cluster G1{G2} of two highly symmetric graphs G1,G2, in terms of the parameters of the original graphs. We also discuss some necessary conditions for a graph to be highly symmetric.

Suggested Citation

  • Palacios, José Luis & Markowsky, Greg, 2021. "Kemeny’s constant and the Kirchhoff index for the cluster of highly symmetric graphs," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    • Handle: RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003726
    DOI: 10.1016/j.amc.2021.126283
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    References listed on IDEAS

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    1. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "The normalized Laplacian spectrum of subdivisions of a graph," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 250-256.
    2. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "On the spectrum of the normalized Laplacian of iterated triangulations of graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1123-1129.
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    Cited by:

    1. Sun, Wensheng & Yang, Yujun, 2023. "Extremal pentagonal chains with respect to the Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 437(C).

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