2022/09/25 by Dong Liu. Pingshan Li, Li, Dong Liu. Pingshan, Bicheng Zhang +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2209.12126
openalex publication_date 2022/09/25 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
The edge-fault-tolerance of networks is of great significance to the design and maintenance of networks. For any pair of vertices u and v of the connected graph G, if they are connected by min \ °G(u),°G(v)\ edge-disjoint paths, then G is strong Menger edge connected (SM-λ for short). The conditional edge-fault-tolerance about the SM- λ property of G, written smλr(G), is the maximum value of m such that G-F is still SM-λ for any edge subset F with |F|≤ m and δ(G-F)≥ r, where δ(G-F) is the minimum degree of G-F. Previously, most of the exact value for smλr(G) is aimed at some well-known networks when r≤ 2, and a few of the lower bounds on some well-known networks for r≥ 3. In this paper, we firstly determine the exact value of smλr(G) on class of hypercube-like networks (HL-networks for short, including hypercubes, twisted cubes, crossed cubes etc.) for a general r, that is, smλr(Gn)=2r(n-r)-n for every Gn∈ HLn, where n≥ 3 and 1≤ r ≤ n-2.