IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v430y2022ics0096300322003319.html
   My bibliography  Save this article

Reliability evaluation of Modified bubble-sort graph networks based on structure fault pattern

Author

Listed:
  • Wang, Na
  • Meng, Jixiang
  • Tian, Yingzhi

Abstract

Let G be a graph and H be a fixed connected subgraph. Let H={H1,H2,⋯,Hk} be a set of connected subgraphs of G. The H-structure connectivity (resp. H-substructure connectivity) κ(G;H) (resp. κs(G;H)) is defined as the least cardinality of H such that Hi is isomorphic to H (resp. a connected subgraph of H) for any 1≤i≤k, and H’s deletion makes G disconnected or trivial. As an extension of the classic connectivity, the H-structure (resp. H-substructure) connectivity can better evaluate the fault-tolerance of an interconnection network. In this paper, we focus on the n-dimensional modified bubble-sort graph MBn. We determine κ(MBn;Pl) (resp. κs(MBn;Pl), where n≥5, 2≤l≤2n, and Pl is a path on l vertices; κ(MBn;C2l) (resp. κs(MBn;C2l)), where 6≤2l≤n, and C2l is a cycle on 2l vertices; κ(MBn;T2l) (resp. κs(MBn;T2l)), where 1≤l≤n−2 and T2l is an l-leaves 2-step star. In addition, we give the upper bound of κ(MBn;K1,l) (resp. κs(MBn;K1,l)), where n≥4 and 2≤l≤n and K1,l is a star on l+1 vertices, and prove that the upper bounds are sharp for l=2,3,4.

Suggested Citation

  • Wang, Na & Meng, Jixiang & Tian, Yingzhi, 2022. "Reliability evaluation of Modified bubble-sort graph networks based on structure fault pattern," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003319
    DOI: 10.1016/j.amc.2022.127257
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322003319
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127257?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Guozhen & Wang, Dajin, 2021. "The structure fault tolerance of arrangement graphs," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    2. Li, Xiaowang & Zhou, Shuming & Ren, Xiangyu & Guo, Xia, 2021. "Structure and substructure connectivity of alternating group graphs," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    3. Lei, Yafei & Meng, Jixiang, 2020. "Structure Fault-tolerance of Arrangement Graphs," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Yihong & Meng, Jixiang & Fan, Jianxi, 2023. "Reliabilities for two kinds of graphs with smaller diameters," Applied Mathematics and Computation, Elsevier, vol. 446(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ba, Lina & Zhang, Heping, 2023. "Structure connectivity of data center networks," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Wang, Yihong & Meng, Jixiang & Fan, Jianxi, 2023. "Reliabilities for two kinds of graphs with smaller diameters," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    3. Zhang, Guozhen & Wang, Dajin, 2021. "The structure fault tolerance of arrangement graphs," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    4. 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).
    5. Wei Feng & Shiying Wang, 2020. "The Diagnosability of Wheel Networks with Missing Edges under the Comparison Model," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    6. Cheng, Dongqin, 2022. "Two disjoint cycles of various lengths in alternating group graph," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    7. Lei, Yafei & Meng, Jixiang, 2020. "Structure Fault-tolerance of Arrangement Graphs," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    8. Li, Xiaowang & Zhou, Shuming & Ren, Xiangyu & Guo, Xia, 2021. "Structure and substructure connectivity of alternating group graphs," Applied Mathematics and Computation, Elsevier, vol. 391(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003319. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.