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On extra connectivity and extra edge-connectivity of balanced hypercubes

Author

Listed:
  • Yang, Da-Wei
  • Feng, Yan-Quan
  • Lee, Jaeun
  • Zhou, Jin-Xin

Abstract

Given a graph G and a non-negative integer h, the h-extra connectivity (or h-extra edge-connectivity, resp.) of G, denoted by κh(G) (or λh(G), resp.), is the minimum cardinality of a set of vertices (or edges, resp.) in G, if it exists, whose deletion disconnects G and leaves each remaining component with more than h vertices. In this paper, we obtain a tight upper bound of the h-extra connectivity and the h-extra edge-connectivity of n-dimensional balanced hypercubes BHn for n ≥ 2 and h≤2n−1. As an application, we prove that κ4(BHn)=κ5(BHn)=6n−8 and λ3(BHn)=8n−8, which improves the previously known results given by Yang (2012) and Lü (2017).

Suggested Citation

  • Yang, Da-Wei & Feng, Yan-Quan & Lee, Jaeun & Zhou, Jin-Xin, 2018. "On extra connectivity and extra edge-connectivity of balanced hypercubes," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 464-473.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:464-473
    DOI: 10.1016/j.amc.2017.10.005
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    Cited by:

    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. Balbuena, C. & Marcote, X., 2019. "The p-restricted edge-connectivity of Kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 258-267.

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