Component edge connectivity of the folded hypercube

2018/03/04 by Shu-Li Zhao, Weihua Yang, Zhao, Shuli +1
Computer Science · Engineering · #Advanced Graph Theory Research #Advancements in Battery Materials #Combinatorics (math.CO) #FOS: Mathematics #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.1803.01312

openalex publication_date 2018/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The g-component edge connectivity cλ_g(G) of a non-complete graph G is the minimum number of edges whose deletion results in a graph with at least g components. In this paper, we determine the component edge connectivity of the folded hypercube cλ_g+1(FQ_n)=(n+1)g-(∑_i=0^st_i2^t_i-1+∑_i=0^s i⋅ 2^t_i) for g≤ 2^[\fracn+12] and n≥ 5, where g be a positive integer and g=∑_i=0^s2^t_i be the decomposition of g such that t₀=[log₂g], and t_i=[log₂(g-∑_r=0^i-12^t_r)] for i≥ 1.

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