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Structure connectivity of data center networks

Author

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  • Ba, Lina
  • Zhang, Heping

Abstract

Last decade, numerous giant data center networks are built to provide increasingly fashionable web applications. For two integers m≥0 and n≥2, the m-dimensional DCell network with n-port switches Dm,n and n-dimensional BCDC network Bn have been proposed. As a generalization of connectivity, structure (substructure) connectivity was recently proposed. Let G and H be two connected graphs. Let F be a set whose elements are subgraphs of G, and every member of F is isomorphic to H (resp. a connected subgraph of H). Then H-structure connectivity κ(G;H) (resp. H-substructure connectivity κs(G;H)) of G is the size of a smallest set of F such that G−F is disconnected or the singleton. Then it is meaningful to calculate the structure connectivity of data center networks on some common structures, such as star K1,t, path Pk, cycle Ck, complete graph Ks and so on. In this paper, we obtain that κ(Dm,n;K1,t)=κs(Dm,n;K1,t)=⌈n−11+t⌉+m for 1≤t≤m+n−2 and κ(Dm,n;Ks)=⌈n−1s⌉+m for 3≤s≤n−1 by analyzing the structural properties of Dm,n. We also compute κ(Bn;H) and κs(Bn;H) for H∈{K1,t,Pk,Ck|1≤t≤2n−3,6≤k≤2n−1} and n≥5 by using g-extra connectivity of Bn.

Suggested Citation

  • Ba, Lina & Zhang, Heping, 2023. "Structure connectivity of data center networks," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    • Handle: RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323001911
    DOI: 10.1016/j.amc.2023.128022
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    References listed on IDEAS

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    1. 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).
    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. 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).

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