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Random walks on edge-transitive graphs (II)

Author

Listed:
  • Palacios, José Luis
  • Renom, José Miguel
  • Berrizbeitia, Pedro

Abstract

We give formulas, in terms of the number of pure k-cycles, for the expected hitting times between vertices at distances greater than 1 for random walks on edge-transitive graphs, extending our prior results for neighboring vertices and also extending results of Devroye-Sbihi and Biggs concerning distance-regular graphs. We apply these formulas to a class of Cayley graphs and give explicit values for the expected hitting times.

Suggested Citation

  • Palacios, José Luis & Renom, José Miguel & Berrizbeitia, Pedro, 1999. "Random walks on edge-transitive graphs (II)," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 25-32, May.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:1:p:25-32
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    References listed on IDEAS

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    1. Palacios, JoséLuis & Renom, JoséMiguel, 1998. "Random walks on edge transitive graphs," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 29-34, January.
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    Cited by:

    1. González-Arévalo, Bárbara & Palacios, José Luis, 1999. "Expected hitting times for random walks on weak products of graphs," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 33-39, May.
    2. Kiyoshi Inoue & Sigeo Aki & Balakrishnan Narayanaswamy, 2013. "Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 349-362, June.
    3. Haiyan, Chen & Fuji, Zhang, 2004. "The expected hitting times for graphs with cutpoints," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 9-17, January.
    4. S. Madhumitha & Sudev Naduvath, 2023. "Graphs Defined on Rings: A Review," Mathematics, MDPI, vol. 11(17), pages 1-80, August.

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    1. Palacios, José Luis & Renom, José M., 2012. "On partial sums of hitting times," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 783-785.
    2. Haiyan, Chen & Fuji, Zhang, 2004. "The expected hitting times for graphs with cutpoints," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 9-17, January.
    3. González-Arévalo, Bárbara & Palacios, José Luis, 1999. "Expected hitting times for random walks on weak products of graphs," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 33-39, May.
    4. Miguel Río & José Luis Palacios, 2016. "Decomposing Hitting Times of Walks on Graphs into Simpler Ones," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1035-1042, December.
    5. S. Madhumitha & Sudev Naduvath, 2023. "Graphs Defined on Rings: A Review," Mathematics, MDPI, vol. 11(17), pages 1-80, August.

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