2022/03/24 by Mingzu Zhang, Zhang, Mingzu, Zhaoxia Tian +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2203.12916
openalex publication_date 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Reliability evaluation and fault tolerance of an interconnection network of some parallel and distributed systems are discussed separately under various link-faulty hypotheses in terms of different P-conditional edge-connectivity. With the help of edge isoperimetric problem's method in combinatorics, this paper mainly offers a novel and unified view to investigate the P-conditional edge-connectivities of hamming graph KLn with satisfying the property that each minimum P-conditional edge-cut separates the KLn just into two components, such as Lt-extra edge-connectivity, t-embedded edge-connectivity, cyclic edge-connectivity, (L-1)t-super edge-connectivity, (L-1)t-average edge-connectivity and Lt-th isoperimetric edge-connectivity. They share the same values in form of (L-1)(n-t)Lt (except for cyclic edge-connectivity), which equals to the minimum number of links-faulty resulting in an L-ary-n-dimensional sub-layer from KLn. Besides, we also obtain the exact values of h-extra edge-connectivity and h-th isoperimetric edge-connectivity of hamming graph KLn for each h≤ L^\lfloor (n)/(2) \rfloor. For the case L=2, K2n=Qn is n-dimensional hypercube. Our results can be applied to more generalized class of networks, called n-dim-ensional bijective connection networks, which contains hypercubes, twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and so on. Our results improve several previous results on this topic.