## Lü, Huazhong and Wu, Tingzeng - Super edge-connectivity and matching preclusion of data center networks

dmtcs:4689 - Discrete Mathematics & Theoretical Computer Science, July 30, 2019, vol. 21 no. 4 - https://doi.org/10.23638/DMTCS-21-4-2
Super edge-connectivity and matching preclusion of data center networks

Authors: Lü, Huazhong and Wu, Tingzeng

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 $n\geq2$.

Volume: vol. 21 no. 4
Section: Graph Theory
Published on: July 30, 2019
Submitted on: July 17, 2018
Keywords: Mathematics - Combinatorics,Computer Science - Discrete Mathematics,05C60, 68R10

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