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Generalized Closeness and Decay Stability of Some Graphs

Author

Listed:
  • Darja Rupnik Poklukar

    (The Faculty of Mechanical Engineering (FME), University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia
    These authors contributed equally to this work.)

  • Janez Žerovnik

    (The Faculty of Mechanical Engineering (FME), University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia
    Rudolfovo—Scientific and Technological Center Novo Mesto, Podbreznik 15, 8000 Novo Mesto, Slovenia
    These authors contributed equally to this work.)

Abstract

Generalized closeness is a recently defined centrality measure. Decay stability, based on generalized closeness, has been previously studied, leading to several conjectures on the decay stability of certain graph classes. In this work, we disprove two of these conjectures by showing that the Cartesian and strong products of paths are not decay stable.

Suggested Citation

  • Darja Rupnik Poklukar & Janez Žerovnik, 2025. "Generalized Closeness and Decay Stability of Some Graphs," Mathematics, MDPI, vol. 13(6), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:939-:d:1610613
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    References listed on IDEAS

    as
    1. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    2. 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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