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The 3-path-connectivity of the k-ary n-cube

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  • Zhu, Wen-Han
  • Hao, Rong-Xia
  • Feng, Yan-Quan
  • Lee, Jaeun

Abstract

Let G be a connected simple graph with vertex set V(G). Let Ω be a subset with cardinality at least two of V(G). A path containing all vertices of Ω is said to be an Ω-path of G. Two Ω-paths T1 and T2 of G are internally disjointif V(T1)∩V(T2)=Ω and E(T1)∩E(T2)=∅. For an integer ℓ with 2≤ℓ, the ℓ-path-connectivityπℓ(G) is defined as πℓ(G)=min{πG(Ω)|Ω⊆V(G) and |Ω|=ℓ}, where πG(Ω) represents the maximum number of internally disjoint Ω-paths. In this paper, we completely determine 3-path-connectivity of the k-ary n-cube Qnk. By deeply exploring the structural proprieties of Qnk, we show that π3(Qnk)=⌊6n−14⌋ with n≥1 and k≥3.

Suggested Citation

  • Zhu, Wen-Han & Hao, Rong-Xia & Feng, Yan-Quan & Lee, Jaeun, 2023. "The 3-path-connectivity of the k-ary n-cube," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005732
    DOI: 10.1016/j.amc.2022.127499
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    References listed on IDEAS

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    1. Li, Yinkui & Gu, Ruijuan & Lei, Hui, 2019. "The generalized connectivity of the line graph and the total graph for the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 645-652.
    2. Li, Shasha & Zhao, Yan & Li, Fengwei & Gu, Ruijuan, 2019. "The generalized 3-connectivity of the Mycielskian of a graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 882-890.
    3. Li, Hengzhe & Ma, Yingbin & Yang, Weihua & Wang, Yifei, 2017. "The generalized 3-connectivity of graph products," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 77-83.
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    Cited by:

    1. Zhou, Qianru & Liu, Hai & Cheng, Baolei & Wang, Yan & Han, Yuejuan & Fan, Jianxi, 2024. "Fault tolerance of recursive match networks based on g-good-neighbor fault pattern," Applied Mathematics and Computation, Elsevier, vol. 461(C).

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