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Note on reliability evaluation of arrangement graphs

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

Abstract

The Rh-restricted connectivity κh is a significant measurement to estimate the reliability of large-scale processor system. The arrangement graph An,k is a generalization and also a competitive alternative of the star graph Sn. In this paper, for any non-negative integer h≤n−2, we determine that κh(An,2)=n(n−2)/2 provided h is odd with h=n−3, otherwise κh(An,2)=(h+2)(n−2)−⌊h2/2+h⌋. This result implies the upper bound of κh(An,k) given by Cheng et al. (J. Supercomput., 73(8)(2017) 3669–3682) is not optimal in a sense.

Suggested Citation

  • Li, Xiang-Jun & Zeng, Xue-Qian & Xu, Jun-Ming, 2022. "Note on reliability evaluation of arrangement graphs," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009280
    DOI: 10.1016/j.amc.2021.126845
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    References listed on IDEAS

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    1. Lei, Yafei & Meng, Jixiang, 2020. "Structure Fault-tolerance of Arrangement Graphs," Applied Mathematics and Computation, Elsevier, vol. 381(C).
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