On conditional fault tolerance of hierarchical cubic networks

2017/09/06 by Xiang-Jun Li, Min Liu, Li, Xiang-Jun +5
Computer Science · Materials Science · #Combinatorics (math.CO) #Distributed systems and fault tolerance #FOS: Mathematics #Interconnection Networks and Systems #Supercapacitor Materials and Fabrication

paper · pdf · doi:10.48550/arxiv.1709.02013

openalex publication_date 2017/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the conditional fault tolerance, h-super connectivity κ^h and h-super edge-connectivity λ^h of the hierarchical cubic network HCN_n, an attractive alternative network to the hypercube, and shows κ^h(HCN_n)=λ^h(HCN_n)=2^h(n+1-h) for any h with 0≤ h≤ n-1. The results imply that at least 2^h(n+1-h) vertices or edges have to be removed from HCN_n to make it disconnected with no vertices of degree less than h, and generalize some known results.

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