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, λ_h(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 concentrate on a constant 2ⁿ⁻¹ for each integer {11×2ⁿ⁻¹}{48} ≤ h ≤ 2ⁿ⁻¹ and n≥ 9. That is, for about 77.083 percent values of h≤2ⁿ⁻¹, the corresponding h-extra edge-connectivity of Qn,2, λ_h(Qn,2), presents a concentration phenomenon. Moreover, the above lower and upper bounds of h are both tight.
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Sun et al. (2024) studied this question.
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