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On the global strong resilience of fault Hamiltonian graphs

Author

Listed:
  • Liu, Huiqing
  • Zhang, Ruiting
  • Zhang, Shunzhe

Abstract

The global strong resilience of G with respect to having a fractional perfect matching, also called FSMP number of G, is the minimum number of edges (or resp., edges and/or vertices) whose deletion results in a graph that has no fractional perfect matchings. A graph G is said to be f-fault Hamiltonian if there exists a Hamiltonian cycle in G−F for any set F of edges and/or vertices with |F|≤f. In this paper, we first give a sufficient condition, involving the independent number, to determine the FSMP number of (δ−2)-fault Hamiltonian graphs with minimum degree δ≥2, and then we can derive the FSMP number of some networks, which generalize some known results.

Suggested Citation

  • Liu, Huiqing & Zhang, Ruiting & Zhang, Shunzhe, 2022. "On the global strong resilience of fault Hamiltonian graphs," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009243
    DOI: 10.1016/j.amc.2021.126841
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    References listed on IDEAS

    as
    1. Yan Liu & Weiwei Liu, 2017. "Fractional matching preclusion of graphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 522-533, August.
    2. Shunzhe Zhang & Huiqing Liu & Dong Li & Xiaolan Hu, 2019. "Fractional matching preclusion of the restricted HL-graphs," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1143-1154, November.
    Full references (including those not matched with items on IDEAS)

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