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The structure fault tolerance of arrangement graphs

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  • Zhang, Guozhen
  • Wang, Dajin

Abstract

The arrangement graph An,k is a prominent underlying topology for multi-processor/multi-computer networks. In this paper, we study the structure fault tolerance of An,k for two structures of interest and significance - the m-leaves starSm, and the m-leaves 2-step starT2m. Let G be a connected graph and H a connected subgraph of G. The H-structure connectivityκ(G;H) (resp. H-substructure connectivityκs(G;H)) of G is the cardinality of a minimum collection F={H1,H2,…,Ht}, such that for each and every 1≤i≤t,Hi⊆G and Hi is isomorphic to H (resp. isomorphic to a connected subgraph of H), and the removal of F disconnects G. In this paper, we will determine κ(An,k;H) and κs(An,k;H) for H∈{Sm,T2m}. Our result adds to the many known, desirable properties of An,k, providing more perspectives when considering its candidacy as an interconnection network for multiprocessor systems.

Suggested Citation

  • Zhang, Guozhen & Wang, Dajin, 2021. "The structure fault tolerance of arrangement graphs," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000874
    DOI: 10.1016/j.amc.2021.126039
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    References listed on IDEAS

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    1. Yuan-Hsiang Teng & Jimmy J. M. Tan & Chey-Woei Tsay & Lih-Hsing Hsu, 2012. "The paths embedding of the arrangement graphs with prescribed vertices in given position," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 627-646, November.
    2. 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).

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