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Structure Fault-tolerance of Arrangement Graphs

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  • Lei, Yafei
  • Meng, Jixiang

Abstract

Given a connected graph G and a connected subgraph H of G. The H-structure connectivity κ(G; H) of G is the minimal cardinality of a set of subgraphs F={J1,J2,…,Jm} in G, where Ji ≅H (1 ≤ i ≤ m), and the deletion of F disconnects G. Similarly, the H-substructure connectivity κs(G; H) of G is the minimal cardinality of a set of subgraphs F={J1,…,Jm} in G, where Ji (1 ≤ i ≤ m) is isomorphic to a connected subgraph of H, and the deletion of F disconnects G. Structure connectivity and substructure connectivity generalize the classical vertex-connectivity. In this thesis, we establish κ(An,k; H) and κs(An,k; H) of the (n, k)-arrangement graph An,k, where H∈{K1,m1,Pm2}(m1≥1,m2≥4).

Suggested Citation

  • Lei, Yafei & Meng, Jixiang, 2020. "Structure Fault-tolerance of Arrangement Graphs," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    • Handle: RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302563
    DOI: 10.1016/j.amc.2020.125287
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    References listed on IDEAS

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    1. 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, 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).
    2. 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).

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