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Reliabilities for two kinds of graphs with smaller diameters

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  • Wang, Yihong
  • Meng, Jixiang
  • Fan, Jianxi

Abstract

Two crucial parameters to be considered when evaluating a network’s reliability are its connectivity and diagnosability. The connectivity of a graph is defined as the smallest number of vertices that, if removed, would leave a disconnected or single-vertex graph. The diagnosability is the maximum number of faulty vertices that the system can correctly identify. In this paper, aim to obtain the reliability of various graphs (e.g. interconnection networks and data center networks), we propose two kinds of graphs (resp. networks)—matching recursive graphs (MRGs) and recursive networks based on connected graphs (RNCGs). We prove that these two kinds of graphs have smaller diameters. Furthermore, we study their reliabilities, including connectivities and diagnosabilities. Moreover, we also extend our results to many graphs.

Suggested Citation

  • Wang, Yihong & Meng, Jixiang & Fan, Jianxi, 2023. "Reliabilities for two kinds of graphs with smaller diameters," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    • Handle: RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000437
    DOI: 10.1016/j.amc.2023.127874
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    References listed on IDEAS

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    1. Chen, Laihuan & Meng, Jixiang & Tian, Yingzhi & Liang, Xiaodong & Liu, Fengxia, 2018. "Connectivity of half vertex transitive digraphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 25-29.
    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. 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).
    4. Liu, Xuemei & Meng, Jixiang, 2021. "The k-restricted edge-connectivity of the data center network DCell," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    5. 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)

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    Keywords

    Reliability; MRG; RNCG; Hypercube; DCell;
    All these keywords.

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