Analysis shows critical reliability parameters in hypercube networks with faulty links, suggesting design improvements for multiprocessor systems.
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 11×2ⁿ⁻¹48 ≤ 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.
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Sun et al. (2025) studied this question.
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