Classes of Planar Graphs with Constant Edge Metric Dimension
The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them. For a vertex x and an edge e=ab in G, the minimum number from distances of x with a and b is said to be the distance between x and e...
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| Main Authors: | , , , , |
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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/10.1155/2021/5599274 |
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| _version_ | 1832547706907656192 |
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| author | Changcheng Wei Muhammad Salman Syed Shahzaib Masood Ur Rehman Juanyan Fang |
| author_facet | Changcheng Wei Muhammad Salman Syed Shahzaib Masood Ur Rehman Juanyan Fang |
| author_sort | Changcheng Wei |
| collection | DOAJ |
| description | The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them. For a vertex x and an edge e=ab in G, the minimum number from distances of x with a and b is said to be the distance between x and e. A vertex x is said to distinguish (resolves) two distinct edges e1 and e2 if the distance between x and e1 is different from the distance between x and e2. A set X of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertex in X. The number of vertices in such a smallest set X is known as the edge metric dimension of G. In this article, we solve the edge metric dimension problem for certain classes of planar graphs. |
| format | Article |
| id | doaj-art-667f53520401433aa5b3323acc9c67c6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-667f53520401433aa5b3323acc9c67c62025-02-03T06:43:45ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/55992745599274Classes of Planar Graphs with Constant Edge Metric DimensionChangcheng Wei0Muhammad Salman1Syed Shahzaib2Masood Ur Rehman3Juanyan Fang4Institute of Mathematics and Computer Science, Tongling College, Tongling 244000, ChinaDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Basic Sciences, Balochistan University of Engineering and Technology Khuzdar, Khuzdar 89100, PakistanInstitute of Mathematics and Computer Science, Tongling College, Tongling 244000, ChinaThe number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph G is known as the distance between them. For a vertex x and an edge e=ab in G, the minimum number from distances of x with a and b is said to be the distance between x and e. A vertex x is said to distinguish (resolves) two distinct edges e1 and e2 if the distance between x and e1 is different from the distance between x and e2. A set X of vertices in a connected graph G is an edge metric generator for G if every two edges of G are distinguished by some vertex in X. The number of vertices in such a smallest set X is known as the edge metric dimension of G. In this article, we solve the edge metric dimension problem for certain classes of planar graphs.http://dx.doi.org/10.1155/2021/5599274 |
| spellingShingle | Changcheng Wei Muhammad Salman Syed Shahzaib Masood Ur Rehman Juanyan Fang Classes of Planar Graphs with Constant Edge Metric Dimension Complexity |
| title | Classes of Planar Graphs with Constant Edge Metric Dimension |
| title_full | Classes of Planar Graphs with Constant Edge Metric Dimension |
| title_fullStr | Classes of Planar Graphs with Constant Edge Metric Dimension |
| title_full_unstemmed | Classes of Planar Graphs with Constant Edge Metric Dimension |
| title_short | Classes of Planar Graphs with Constant Edge Metric Dimension |
| title_sort | classes of planar graphs with constant edge metric dimension |
| url | http://dx.doi.org/10.1155/2021/5599274 |
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