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On the residual closeness of graphs with cut vertices

Author

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  • Chengli Li

    (South China Normal University)

  • Leyou Xu

    (South China Normal University)

  • Bo Zhou

    (South China Normal University)

Abstract

In designing and understanding of computer networks, how to improve network robustness or protect a network from vulnerability remains an overarching concern. The residual closeness is a measure of network vulnerability and robustness even when the removal of vertices does not disconnect the underlying graph. We determine all the graphs that minimize and maximize the residual closeness respectively over all n-vertex connected graphs with r cut vertices, where $$1\le r\le n-3$$ 1 ≤ r ≤ n - 3 .

Suggested Citation

  • Chengli Li & Leyou Xu & Bo Zhou, 2023. "On the residual closeness of graphs with cut vertices," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-24, July.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:5:d:10.1007_s10878-023-01042-5
    DOI: 10.1007/s10878-023-01042-5
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    References listed on IDEAS

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    1. Dangalchev, Chavdar, 2006. "Residual closeness in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 556-564.
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    Cited by:

    1. Fazal Hayat & Daniele Ettore Otera, 2024. "Maximizing Closeness in Bipartite Networks: A Graph-Theoretic Analysis," Mathematics, MDPI, vol. 12(13), pages 1-13, June.

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