Super edge-connectivity and matching preclusion of data center networks
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 ro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2019-07-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/4689/pdf |
| _version_ | 1797270013176971264 |
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| author | Huazhong Lü Tingzeng Wu |
| author_facet | Huazhong Lü Tingzeng Wu |
| author_sort | Huazhong Lü |
| collection | DOAJ |
| description | 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 $n\geq2$. |
| first_indexed | 2024-04-25T01:57:31Z |
| format | Article |
| id | doaj.art-8282dc6f3ab049b6bdecccab5f5e40c9 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:57:31Z |
| publishDate | 2019-07-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-8282dc6f3ab049b6bdecccab5f5e40c92024-03-07T15:40:07ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502019-07-01vol. 21 no. 4Graph Theory10.23638/DMTCS-21-4-24689Super edge-connectivity and matching preclusion of data center networksHuazhong LüTingzeng WuEdge-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 $n\geq2$.https://dmtcs.episciences.org/4689/pdfmathematics - combinatoricscomputer science - discrete mathematics05c60, 68r10 |
| spellingShingle | Huazhong Lü Tingzeng Wu Super edge-connectivity and matching preclusion of data center networks Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics computer science - discrete mathematics 05c60, 68r10 |
| title | Super edge-connectivity and matching preclusion of data center networks |
| title_full | Super edge-connectivity and matching preclusion of data center networks |
| title_fullStr | Super edge-connectivity and matching preclusion of data center networks |
| title_full_unstemmed | Super edge-connectivity and matching preclusion of data center networks |
| title_short | Super edge-connectivity and matching preclusion of data center networks |
| title_sort | super edge connectivity and matching preclusion of data center networks |
| topic | mathematics - combinatorics computer science - discrete mathematics 05c60, 68r10 |
| url | https://dmtcs.episciences.org/4689/pdf |
| work_keys_str_mv | AT huazhonglu superedgeconnectivityandmatchingpreclusionofdatacenternetworks AT tingzengwu superedgeconnectivityandmatchingpreclusionofdatacenternetworks |