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Generalized measures of fault tolerance for bubble sort networks

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  • Li, Xiang-Jun
  • Zeng, Xue-Qian
  • Xu, Jun-Ming

Abstract

The κk and λk are two generalized measurements for fault tolerance of large-scale processing system. For the bubble sort networks Bn, this paper determines κk(Bn)=λk(Bn)=2k(n−k−1) for k ≤ n/2. The results show that to disconnect Bn with each vertex in resulting graph has at least k fault-free neighbors, at least 2k(n−k−1) faulty vertices or faulty edges have to occur. In particular, the results also settle affirmatively a conjecture proposed by Shi and Wu (Acta Math. Appl. Sin-E., 33 (4)(2017), 933–944).

Suggested Citation

  • Li, Xiang-Jun & Zeng, Xue-Qian & Xu, Jun-Ming, 2019. "Generalized measures of fault tolerance for bubble sort networks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:29
    DOI: 10.1016/j.amc.2019.124630
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    References listed on IDEAS

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    1. Zhao, Shu-Li & Hao, Rong-Xia, 2019. "The generalized 4-connectivity of exchanged hypercubes," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 342-353.
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