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

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摘要

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

论文关键词：Electric networks,Kemeny constant,Kirchhoff index,Random walks,Highly symmetric graphs

论文评审过程：Received 14 June 2020, Revised 3 April 2021, Accepted 6 April 2021, Available online 24 April 2021, Version of Record 24 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126283