Super edge-connectivity and matching preclusion of data center networks
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Edge-connectivity is a classic measure for reliability of a network in the presence of edge failures. k-restricted edge-connectivity is one of the refined indicators for fault tolerance of large networks. Matching preclusion and conditional matching preclusion are two important measures for the robustness of networks in edge fault scenario. In this paper, we show that the DCell network D_k,n is super-λ for k≥2 and n≥2, super-λ_2 for k≥3 and n≥2, or k=2 and n=2, and super-λ_3 for k≥4 and n≥3. Moreover, as an application of k-restricted edge-connectivity, we study the matching preclusion number and conditional matching preclusion number, and characterize the corresponding optimal solutions of D_k,n. In particular, we have shown that D_1,n is isomorphic to the (n,k)-star graph S_n+1,2 for n≥2.
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