Geodesic
Super edge-connectivity and matching preclusion of data center networks
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4.

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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-$\lambda$ for $k\geq2$ and $n\geq2$, super-$\lambda_2$ for $k\geq3$ and $n\geq2$, or $k=2$ and $n=2$, and super-$\lambda_3$ for $k\geq4$ and $n\geq3$. 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 $n\geq2$. 
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     author = {L\"u, Huazhong and Wu, Tingzeng},
     title = {Super edge-connectivity and matching preclusion of data center networks},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2019},
     doi = {10.23638/DMTCS-21-4-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-2/}
}
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Lü, Huazhong; Wu, Tingzeng. Super edge-connectivity and matching preclusion of data center networks. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4. doi : 10.23638/DMTCS-21-4-2. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-2/

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