Computing Fault-Tolerant Metric Dimension of Connected Graphs
For a connected graph, the concept of metric dimension contributes an important role in computer networking and in the formation of chemical structures. Among the various types of the metric dimensions, the fault-tolerant metric dimension has attained much more attention by the researchers in the la...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9773089 |
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| _version_ | 1832565477716525056 |
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| author | Uzma Ahmad Sara Ahmed Muhammad Javaid Md Nur Alam |
| author_facet | Uzma Ahmad Sara Ahmed Muhammad Javaid Md Nur Alam |
| author_sort | Uzma Ahmad |
| collection | DOAJ |
| description | For a connected graph, the concept of metric dimension contributes an important role in computer networking and in the formation of chemical structures. Among the various types of the metric dimensions, the fault-tolerant metric dimension has attained much more attention by the researchers in the last decade. In this study, the mixed fault-tolerant dimension of rooted product of a graph with path graph with reference to a pendant vertex of path graph is determined. In general, the necessary and sufficient conditions for graphs of order at least 3 having mixed fault-tolerant generators are established. Moreover, the mixed fault-tolerant metric generator is determined for graphs having shortest cycle length at least 4. |
| format | Article |
| id | doaj-art-e47b9315b446452a8717dd565f9cc967 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e47b9315b446452a8717dd565f9cc9672025-02-03T01:07:37ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9773089Computing Fault-Tolerant Metric Dimension of Connected GraphsUzma Ahmad0Sara Ahmed1Muhammad Javaid2Md Nur Alam3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsFor a connected graph, the concept of metric dimension contributes an important role in computer networking and in the formation of chemical structures. Among the various types of the metric dimensions, the fault-tolerant metric dimension has attained much more attention by the researchers in the last decade. In this study, the mixed fault-tolerant dimension of rooted product of a graph with path graph with reference to a pendant vertex of path graph is determined. In general, the necessary and sufficient conditions for graphs of order at least 3 having mixed fault-tolerant generators are established. Moreover, the mixed fault-tolerant metric generator is determined for graphs having shortest cycle length at least 4.http://dx.doi.org/10.1155/2022/9773089 |
| spellingShingle | Uzma Ahmad Sara Ahmed Muhammad Javaid Md Nur Alam Computing Fault-Tolerant Metric Dimension of Connected Graphs Journal of Mathematics |
| title | Computing Fault-Tolerant Metric Dimension of Connected Graphs |
| title_full | Computing Fault-Tolerant Metric Dimension of Connected Graphs |
| title_fullStr | Computing Fault-Tolerant Metric Dimension of Connected Graphs |
| title_full_unstemmed | Computing Fault-Tolerant Metric Dimension of Connected Graphs |
| title_short | Computing Fault-Tolerant Metric Dimension of Connected Graphs |
| title_sort | computing fault tolerant metric dimension of connected graphs |
| url | http://dx.doi.org/10.1155/2022/9773089 |
| work_keys_str_mv | AT uzmaahmad computingfaulttolerantmetricdimensionofconnectedgraphs AT saraahmed computingfaulttolerantmetricdimensionofconnectedgraphs AT muhammadjavaid computingfaulttolerantmetricdimensionofconnectedgraphs AT mdnuralam computingfaulttolerantmetricdimensionofconnectedgraphs |