The Strong Local Diagnosability of a Hypercube Network with Missing Edges
In the research on the reliability of a connection network, diagnosability is an important problem that should be considered. In this article, a new concept regarding diagnosability, called strong local diagnosability (SLD), which describes the local status of the strong diagnosability (SD) of a sys...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/5745628 |
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| author | Min Xie Jiarong Liang Xi Xiong |
| author_facet | Min Xie Jiarong Liang Xi Xiong |
| author_sort | Min Xie |
| collection | DOAJ |
| description | In the research on the reliability of a connection network, diagnosability is an important problem that should be considered. In this article, a new concept regarding diagnosability, called strong local diagnosability (SLD), which describes the local status of the strong diagnosability (SD) of a system, is presented. In addition, a few important results related to the SLD of a node of a system are presented. Based on these results, we conclude that in a hypercube network of n dimensions, denoted by Qn, the SLD of a node is equal to its degree when n⩾4. Moreover, we explore the SLD of a node of an incomplete hypercube network. We determine that the SLD of a node is equal to its remaining degree (RD) in an incomplete hypercube network, which is true provided that the number of faulty edges in this hypercube network does not exceed n−3. Finally, we discuss the SLD of a node for an incomplete hypercube network and obtain the following results: if the minimum RD of nodes in an incomplete hypercube network of n-dimensions is greater than 3, then the SLD of any node is still equal to its RD provided that the number of faulty edges does not exceed 7n−3−1. If the RD of each node is greater than 4, then the SLD of each node is also equal to its RD, no matter how many faulty edges exist in Qn. |
| format | Article |
| id | doaj-art-a01d593b0d4c40eaa367f73c5d7418df |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a01d593b0d4c40eaa367f73c5d7418df2025-02-03T06:44:39ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/57456285745628The Strong Local Diagnosability of a Hypercube Network with Missing EdgesMin Xie0Jiarong Liang1Xi Xiong2School of Automation Science and Engineering, South China University of Technology, 510640, ChinaSchool of Computer and Electronics Information, Guangxi University, 530004, ChinaSchool of Computer and Electronics Information, Guangxi University, 530004, ChinaIn the research on the reliability of a connection network, diagnosability is an important problem that should be considered. In this article, a new concept regarding diagnosability, called strong local diagnosability (SLD), which describes the local status of the strong diagnosability (SD) of a system, is presented. In addition, a few important results related to the SLD of a node of a system are presented. Based on these results, we conclude that in a hypercube network of n dimensions, denoted by Qn, the SLD of a node is equal to its degree when n⩾4. Moreover, we explore the SLD of a node of an incomplete hypercube network. We determine that the SLD of a node is equal to its remaining degree (RD) in an incomplete hypercube network, which is true provided that the number of faulty edges in this hypercube network does not exceed n−3. Finally, we discuss the SLD of a node for an incomplete hypercube network and obtain the following results: if the minimum RD of nodes in an incomplete hypercube network of n-dimensions is greater than 3, then the SLD of any node is still equal to its RD provided that the number of faulty edges does not exceed 7n−3−1. If the RD of each node is greater than 4, then the SLD of each node is also equal to its RD, no matter how many faulty edges exist in Qn.http://dx.doi.org/10.1155/2018/5745628 |
| spellingShingle | Min Xie Jiarong Liang Xi Xiong The Strong Local Diagnosability of a Hypercube Network with Missing Edges Complexity |
| title | The Strong Local Diagnosability of a Hypercube Network with Missing Edges |
| title_full | The Strong Local Diagnosability of a Hypercube Network with Missing Edges |
| title_fullStr | The Strong Local Diagnosability of a Hypercube Network with Missing Edges |
| title_full_unstemmed | The Strong Local Diagnosability of a Hypercube Network with Missing Edges |
| title_short | The Strong Local Diagnosability of a Hypercube Network with Missing Edges |
| title_sort | strong local diagnosability of a hypercube network with missing edges |
| url | http://dx.doi.org/10.1155/2018/5745628 |
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