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A Measure for the Vulnerability of Uniform Hypergraph Networks: Scattering Number

Author

Listed:
  • Ning Zhao

    (School of Computer, Qinghai Normal University, Xining 810000, China
    School of Mathematics and Statistics, Qinghai Minzu University, Xining 810000, China)

  • Haixing Zhao

    (School of Computer, Qinghai Normal University, Xining 810000, China)

  • Yinkui Li

    (School of Mathematics and Statistics, Qinghai Minzu University, Xining 810000, China)

Abstract

The scattering number of a graph G is defined as s ( G ) = m a x { ω ( G − X ) − | X | : X ⊂ V ( G ) , ω ( G − X ) > 1 } , where X is a cut set of G , and ω ( G − X ) denotes the number of components in G − X , which can be used to measure the vulnerability of network G . In this paper, we generalize this parameter to a hypergraph to measure the vulnerability of uniform hypergraph networks. Firstly, some bounds on the scattering number are given. Secondly, the relations of scattering number between a complete k -uniform hypergraph and complete bipartite k -uniform hypergraph are discussed.

Suggested Citation

  • Ning Zhao & Haixing Zhao & Yinkui Li, 2024. "A Measure for the Vulnerability of Uniform Hypergraph Networks: Scattering Number," Mathematics, MDPI, vol. 12(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:515-:d:1335114
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    References listed on IDEAS

    as
    1. Alpay Kirlangiç, 2002. "A measure of graph vulnerability: scattering number," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-8, January.
    2. Xiao-Min Zhu & Weijun Liu & Xu Yang, 2023. "Spectral Conditions, Degree Sequences, and Graphical Properties," Mathematics, MDPI, vol. 11(20), pages 1-18, October.
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