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The Hitting Times of Random Walks on Bicyclic Graphs

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Abstract

Let \(H_G(x, y)\) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and \(\varphi (G){:}{=}\max \left\{ H_G(x, y): x, y\in V(G)\right\}\) be called the hitting time of G. In this paper, sharp upper and lower bounds for \(\varphi (G)\) among all n-vertex bicyclic graphs are presented and the extremal graphs are determined.

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Acknowledgements

The authors would like to thank the referees for their helpful and constructed comments and provide reference [29].

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Authors and Affiliations

  1. School of Mathematical Sciences, MOE-LSC, SHL-MAC, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Xiaomin Zhu & Xiao-Dong Zhang

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  1. Xiaomin Zhu
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  2. Xiao-Dong Zhang
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Correspondence to Xiao-Dong Zhang.

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This work is supported by the National Natural Science Foundation of China (Nos. 11971311, 12026230 and 11531001), the Montenegrin-Chinese Science and Technology Cooperation Project (No. 3-12).

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Zhu, X., Zhang, XD. The Hitting Times of Random Walks on Bicyclic Graphs. Graphs and Combinatorics 37, 2365–2386 (2021). https://doi.org/10.1007/s00373-021-02360-3

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  • DOI: https://doi.org/10.1007/s00373-021-02360-3

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