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

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  • 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
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    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.
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    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).

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