2024/04/26 by Yali Sun, Sun, Yali, Mingzu Zhang +5
Computer Science · Engineering · #Advanced Battery Technologies Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Reliability and Maintenance Optimization #Software Reliability and Analysis Research
paper · pdf · doi:10.48550/arxiv.2404.17150
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The (n, k)-enhanced hypercube Qn,k, as a variation of the hypercube Qn, was proposed by Tzeng and Wei in 1991. As an extension of traditional edge-connectivity, h-extra edge-connectivity of a connected graph G, λh(G), is an essential parameter for evaluating the reliability of interconnection networks. This article intends to study the h-extra edge-connectivity of the (n,2)-enhanced hypercube Qn,2. Suppose that the link malfunction of an interconnection network Qn,2 does not isolate any subnetwork with no more than h-1 processors, the minimum number of these possible faulty links concentrates on a constant 2n-1 for each integer \lceil\frac11×2n-148\rceil ≤ h ≤ 2n-1 and n≥ 9. That is, for about 77.083% of values where h≤2n-1, the corresponding h-extra edge-connectivity of Qn,2, λh(Qn,2), presents a concentration phenomenon. Moreover, the lower and upper bounds of h mentioned above are both tight.