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Two-disjoint-cycle-cover pancyclicity of data center networks

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  • Hao, Rong-Xia
  • Qin, Xiao-Wen
  • Zhang, Hui
  • Chang, Jou-Ming

Abstract

A graph G is two-disjoint-cycle-cover [r1,r2]-pancyclic if for any integer ℓ satisfying r1≤ℓ≤r2, there exist two vertex-disjoint cycles C1 and C2 in G such that |V(C1)|=ℓ and |V(C2)|=|V(G)|−ℓ. The k-dimensional data center network DCell with n port switches and order tk,n, denoted by Dk,n, plays an important role in big data cloud computing. In this paper, we study the structural properties of Dk,n and show that Dk,n is two-disjoint-cycle-cover [3,⌊tk,n2⌋]-pancyclic for n≥7 and n+k≥11, that is, for any integer ℓ satisfying 3≤ℓ≤⌊tk,n2⌋, there exist two vertex-disjoint cycles C1 and C2 such that |V(C1)|=ℓ and |V(C2)|=tk,n−ℓ in Dk,n. This paper generalizes the results about the Hamiltonicity in (Wang et al., 2015 [25]) and the pancyclicity in (Hao and Tian, 2021 [11]).

Suggested Citation

  • Hao, Rong-Xia & Qin, Xiao-Wen & Zhang, Hui & Chang, Jou-Ming, 2024. "Two-disjoint-cycle-cover pancyclicity of data center networks," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    • Handle: RePEc:eee:apmaco:v:475:y:2024:i:c:s0096300324001887
    DOI: 10.1016/j.amc.2024.128716
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    References listed on IDEAS

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    1. Wei, Chao & Hao, Rong-Xia & Chang, Jou-Ming, 2020. "Two-disjoint-cycle-cover bipancyclicity of balanced hypercubes," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    2. Qin, Xiao-Wen & Chang, Jou-Ming & Hao, Rong-Xia, 2019. "Constructing dual-CISTs of DCell data center networks," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Ba, Lina & Zhang, Heping, 2023. "Structure connectivity of data center networks," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    4. Niu, Ruichao & Xu, Min & Lai, Hong-Jian, 2021. "Two-disjoint-cycle-cover vertex bipancyclicity of the bipartite generalized hypercube," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    5. Liu, Xuemei & Meng, Jixiang, 2021. "The k-restricted edge-connectivity of the data center network DCell," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    6. Liu, Xuemei & Meng, Jixiang & Sabir, Eminjan, 2023. "Component connectivity of the data center network DCell," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    7. 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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