Structure connectivity and substructure connectivity of data center network
The structure connectivity $ \kappa(G; H) $ and substructure connectivity $ \kappa^s(G; H) $ are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by $ D_{k, n} $, have been proposed for data centers as a server-centric i...
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| Format: | Article |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023499?viewType=HTML |
| _version_ | 1827997201613193216 |
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| author | Bo Zhu Shumin Zhang Jinyu Zou Chengfu Ye |
| author_facet | Bo Zhu Shumin Zhang Jinyu Zou Chengfu Ye |
| author_sort | Bo Zhu |
| collection | DOAJ |
| description | The structure connectivity $ \kappa(G; H) $ and substructure connectivity $ \kappa^s(G; H) $ are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by $ D_{k, n} $, have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain $ \kappa(D_{k, n}; S_m) $ and $ \kappa^s(D_{k, n}; S_m) $ when $ k\geq2 $, $ n\geq4 $ and $ 1\leq m\leq n+k-2 $. Furthermore, we obtain both $ \kappa(D_{k, n}; S_{23}) $ and $ \kappa^s(D_{k, n}; S_{23}) $ for $ k\geq8 $ and $ n\geq8 $.
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| first_indexed | 2024-04-10T05:24:43Z |
| format | Article |
| id | doaj.art-605fcb02d2da4b48a9cddf9dbd129338 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T05:24:43Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-605fcb02d2da4b48a9cddf9dbd1293382023-03-08T01:34:58ZengAIMS PressAIMS Mathematics2473-69882023-02-01849877988910.3934/math.2023499Structure connectivity and substructure connectivity of data center networkBo Zhu0Shumin Zhang 1Jinyu Zou2Chengfu Ye 31. Department of Computer, Qinghai Normal University, Xining, Qinghai 810008, China2. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China4. Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal University3. Department of Basic Research, Qinghai University, Xining, Qinghai 810016, China2. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China4. Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal UniversityThe structure connectivity $ \kappa(G; H) $ and substructure connectivity $ \kappa^s(G; H) $ are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by $ D_{k, n} $, have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain $ \kappa(D_{k, n}; S_m) $ and $ \kappa^s(D_{k, n}; S_m) $ when $ k\geq2 $, $ n\geq4 $ and $ 1\leq m\leq n+k-2 $. Furthermore, we obtain both $ \kappa(D_{k, n}; S_{23}) $ and $ \kappa^s(D_{k, n}; S_{23}) $ for $ k\geq8 $ and $ n\geq8 $. https://www.aimspress.com/article/doi/10.3934/math.2023499?viewType=HTMLstructure connectivitysubstructure connectivitydata center network |
| spellingShingle | Bo Zhu Shumin Zhang Jinyu Zou Chengfu Ye Structure connectivity and substructure connectivity of data center network AIMS Mathematics structure connectivity substructure connectivity data center network |
| title | Structure connectivity and substructure connectivity of data center network |
| title_full | Structure connectivity and substructure connectivity of data center network |
| title_fullStr | Structure connectivity and substructure connectivity of data center network |
| title_full_unstemmed | Structure connectivity and substructure connectivity of data center network |
| title_short | Structure connectivity and substructure connectivity of data center network |
| title_sort | structure connectivity and substructure connectivity of data center network |
| topic | structure connectivity substructure connectivity data center network |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023499?viewType=HTML |
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