On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs
Assume that G=VG,EG is a connected graph. For a set of vertices WE⊆VG, two edges g1,g2∈EG are distinguished by a vertex x1∈WE, if dx1,g1≠dx1,g2. WE is termed edge metric generator for G if any vertex of WE distinguishes every two arbitrarily distinct edges of graph G. Furthermore, the edge metric di...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6738129 |
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| author | Dalal Alrowaili Zohaib Zahid Imran Siddique Sohail Zafar Muhammad Ahsan Muhammad Sarwar Sindhu |
| author_facet | Dalal Alrowaili Zohaib Zahid Imran Siddique Sohail Zafar Muhammad Ahsan Muhammad Sarwar Sindhu |
| author_sort | Dalal Alrowaili |
| collection | DOAJ |
| description | Assume that G=VG,EG is a connected graph. For a set of vertices WE⊆VG, two edges g1,g2∈EG are distinguished by a vertex x1∈WE, if dx1,g1≠dx1,g2. WE is termed edge metric generator for G if any vertex of WE distinguishes every two arbitrarily distinct edges of graph G. Furthermore, the edge metric dimension of G, indicated by edimG, is the cardinality of the smallest WE for G. The edge metric dimensions of the dragon, kayak paddle, cycle with chord, generalized prism, and necklace graphs are calculated in this article. |
| format | Article |
| id | doaj-art-f0cb1196332d45038b08e6e7206ae94b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f0cb1196332d45038b08e6e7206ae94b2025-02-03T05:49:22ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6738129On the Constant Edge Resolvability of Some Unicyclic and Multicyclic GraphsDalal Alrowaili0Zohaib Zahid1Imran Siddique2Sohail Zafar3Muhammad Ahsan4Muhammad Sarwar Sindhu5Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsAssume that G=VG,EG is a connected graph. For a set of vertices WE⊆VG, two edges g1,g2∈EG are distinguished by a vertex x1∈WE, if dx1,g1≠dx1,g2. WE is termed edge metric generator for G if any vertex of WE distinguishes every two arbitrarily distinct edges of graph G. Furthermore, the edge metric dimension of G, indicated by edimG, is the cardinality of the smallest WE for G. The edge metric dimensions of the dragon, kayak paddle, cycle with chord, generalized prism, and necklace graphs are calculated in this article.http://dx.doi.org/10.1155/2022/6738129 |
| spellingShingle | Dalal Alrowaili Zohaib Zahid Imran Siddique Sohail Zafar Muhammad Ahsan Muhammad Sarwar Sindhu On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs Journal of Mathematics |
| title | On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs |
| title_full | On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs |
| title_fullStr | On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs |
| title_full_unstemmed | On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs |
| title_short | On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs |
| title_sort | on the constant edge resolvability of some unicyclic and multicyclic graphs |
| url | http://dx.doi.org/10.1155/2022/6738129 |
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