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Structure and substructure connectivity of alternating group graphs

Author

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  • Li, Xiaowang
  • Zhou, Shuming
  • Ren, Xiangyu
  • Guo, Xia

Abstract

The connectivity is an important indicator to evaluate the robustness of a network. Many works have focused on connectivity-based reliability analysis for decades. As a generalization of connectivity, H-structure connectivity and H-substructure connectivity were proposed to evaluate the robustness of networks. In this paper, we investigate the H-structure connectivity and H-substructure connectivity of alternating group graph AGn when H is isomorphic to K1,t, Pl and Ck, which are generalizations of the previous results for H ∈ {K1, K1,1, K1,2}. And we show that κ(AGn;K1,t)=κs(AGn;K1,t)=n−2 (1≤t≤2n−6),κ(AGn;Pl)=κs(AGn;Pl)=⌈2n−4l−⌊l/3⌋⌉ (1≤l≤3n−7), κ(AGn;Ck)=⌈n−2⌊k/3⌋⌉ and κs(AGn;Ck)=⌈2n−4k−⌊k/3⌋⌉ (6≤k≤3n−6).

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320305932
    DOI: 10.1016/j.amc.2020.125639
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    References listed on IDEAS

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    1. Lily Chen & Xueliang Li & Mengmeng Liu & Yaping Mao, 2017. "A solution to a conjecture on the generalized connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 275-282, January.
    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).
    2. Ba, Lina & Zhang, Heping, 2023. "Structure connectivity of data center networks," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Wang, Yihong & Meng, Jixiang & Fan, Jianxi, 2023. "Reliabilities for two kinds of graphs with smaller diameters," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    4. Cheng, Dongqin, 2022. "Two disjoint cycles of various lengths in alternating group graph," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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