On extra connectivity and extra edge-connectivity of balanced hypercubes

Da-Wei Yang, Yan-Quan Feng, Jaeun Lee and Jin-Xin Zhou

Applied Mathematics and Computation, 2018, vol. 320, issue C, 464-473

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).

Keywords: Interconnection networks; Reliability; Balanced hypercube; Extra connectivity; Extra edge-connectivity (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:464-473

DOI: 10.1016/j.amc.2017.10.005

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