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The g-extra connectivity and diagnosability of crossed cubes

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  • Wang, Shiying
  • Ma, Xiaolei

Abstract

Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network G. In 1996, Fàbrega and Fiol proposed the g-extra connectivity of G. In 2016, Zhang et al. proposed the g-extra diagnosability of G that requires every component of G−S has at least (g+1) vertices. The g-extra connectivity of G is necessary for g-extra diagnosability of G. In this paper, we show that the g-extra connectivity of the crossed cube CQn is n(g+1)−12g(g+3) for n ≥ 5, 0≤g≤⌊n2⌋ and the g-extra diagnosability of CQn is (n−12g)(g+1) under the PMC model for n ≥ 5, 0≤g≤⌊n2⌋ and the MM* model for n ≥ 7, 0≤g≤⌊n2⌋.

Suggested Citation

  • Wang, Shiying & Ma, Xiaolei, 2018. "The g-extra connectivity and diagnosability of crossed cubes," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 60-66.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:60-66
    DOI: 10.1016/j.amc.2018.04.054
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    References listed on IDEAS

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    1. Wang, Shiying & Yang, Yuxing, 2017. "The 2-good-neighbor (2-extra) diagnosability of alternating group graph networks under the PMC model and MM* model," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 241-250.
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    Cited by:

    1. Liu, Qinghai & Hong, Yanmei, 2019. "The reliability of lexicographic product digraphs," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 449-454.
    2. Lin, Shangwei & Zhang, Wenli, 2020. "The 1-good-neighbor diagnosability of unidirectional hypercubes under the PMC model," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    3. Balbuena, C. & Marcote, X., 2019. "The p-restricted edge-connectivity of Kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 258-267.
    4. Zhang, Guozhen & Wang, Dajin, 2019. "Structure connectivity and substructure connectivity of bubble-sort star graph networks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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