The g-extra edge-connectivity of balanced hypercubes

2020/07/06 by Yulong Wei, Rong-Hua Li, Wei, Yulong +3
Computer Science · Engineering · #68M10 #Advanced Battery Technologies Research #Advancements in Battery Materials #Combinatorics (math.CO) #FOS: Mathematics #Interconnection Networks and Systems #Primary 68M15 #Secondary 05C82

paper · pdf · doi:10.48550/arxiv.2007.02522

openalex publication_date 2020/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The g-extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464--473] determined the 3-extra edge-connectivity of balanced hypercubes BH_n and conjectured that the g-extra edge-connectivity of BH_n is λ_g(BH_n)=2(g+1)n-4g+4 for 2≤ g≤ 2n-1. In this paper, we confirm their conjecture for n≥ 6-\dfrac12g+1 and 2≤ g≤ 8, and disprove their conjecture for n≥ \dfrac3e_g(BH_n)g+1 and 9≤ g≤ 2n-1, where e_g(BH_n)=max\|E(BH_n[U])|| U⊆ V(BH_n), |U|=g+1\.

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