Generalized Measures of Fault Tolerance in Exchanged Hypercubes

2012/11/16 by Xiang-Jun Li, Li, Xiang-Jun, Jun‐Ming Xu +2
Computer Science · Mathematics · #Combinatorics (math.CO) #Distributed systems and fault tolerance #FOS: Mathematics #Interconnection Networks and Systems #Software-Defined Networks and 5G #math.CO

paper · pdf · doi:10.48550/arxiv.1211.3814

arxiv created 2012/11/16 · openalex publication_date 2012/11/16 · arxiv updated 2012/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The exchanged hypercube EH(s,t), proposed by Loh \it et al. [The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866-874], is obtained by removing edges from a hypercube Q_s+t+1. This paper considers a kind of generalized measures κ^(h) and λ^(h) of fault tolerance in EH(s,t) with 1\leqslant s\leqslant t and determines κ^(h)(EH(s,t))=λ^(h)(EH(s,t))= 2^h(s+1-h) for any h with 0\leqslant h\leqslant s. The results show that at least 2^h(s+1-h) vertices (resp. 2^h(s+1-h) edges) of EH(s,t) have to be removed to get a disconnected graph that contains no vertices of degree less than h, and generalizes some known results.

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