On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks
In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an arbitrary vertex stopped working and selected...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/9939559 |
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| author | Hua Wang Muhammad Azeem Muhammad Faisal Nadeem Ata Ur-Rehman Adnan Aslam |
| author_facet | Hua Wang Muhammad Azeem Muhammad Faisal Nadeem Ata Ur-Rehman Adnan Aslam |
| author_sort | Hua Wang |
| collection | DOAJ |
| description | In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an arbitrary vertex stopped working and selected vertices still remain the resolving set, then the chosen set is called as the fault-tolerant resolving set. The least number of vertices in such resolving sets is called the fault-tolerant metric dimension of the network. Because of the variety of applications of the metric dimension in different areas of sciences, many generalizations were proposed, and fault tolerant is one of them. In this paper, we computed the fault-tolerant metric dimension of triangular snake, ladder, Mobius ladder, and hexagonal ladder networks. It is important to observe that, in all these classes of networks, the fault-tolerant metric dimension and metric dimension differ by 1. |
| format | Article |
| id | doaj-art-0a1ce5cc1d51491197b9092bc00c8192 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-0a1ce5cc1d51491197b9092bc00c81922025-02-03T05:52:27ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/99395599939559On Fault-Tolerant Resolving Sets of Some Families of Ladder NetworksHua Wang0Muhammad Azeem1Muhammad Faisal Nadeem2Ata Ur-Rehman3Adnan Aslam4School of Mathematics and Statistics Changsha, University of Science and Technology, Changsha 410114, ChinaDepartment of Aerospace Engineering, Faculty of Engineering, University Putra Malaysia, Seri Kembangan, MalaysiaDepartment of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, PakistanDepartment of Electrical Engineering, University of Engineering and Technology, Lahore (RCET), Lahore, PakistanDepartment of Natural Sciences and Humanities, University of Engineering and Technology, Lahore (RCET), Lahore, PakistanIn computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an arbitrary vertex stopped working and selected vertices still remain the resolving set, then the chosen set is called as the fault-tolerant resolving set. The least number of vertices in such resolving sets is called the fault-tolerant metric dimension of the network. Because of the variety of applications of the metric dimension in different areas of sciences, many generalizations were proposed, and fault tolerant is one of them. In this paper, we computed the fault-tolerant metric dimension of triangular snake, ladder, Mobius ladder, and hexagonal ladder networks. It is important to observe that, in all these classes of networks, the fault-tolerant metric dimension and metric dimension differ by 1.http://dx.doi.org/10.1155/2021/9939559 |
| spellingShingle | Hua Wang Muhammad Azeem Muhammad Faisal Nadeem Ata Ur-Rehman Adnan Aslam On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks Complexity |
| title | On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks |
| title_full | On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks |
| title_fullStr | On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks |
| title_full_unstemmed | On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks |
| title_short | On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks |
| title_sort | on fault tolerant resolving sets of some families of ladder networks |
| url | http://dx.doi.org/10.1155/2021/9939559 |
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