The Vertex-Edge Resolvability of Some Wheel-Related Graphs
A vertex w∈VH distinguishes (or resolves) two elements (edges or vertices) a,z∈VH∪EH if dw,a≠dw,z. A set Wm of vertices in a nontrivial connected graph H is said to be a mixed resolving set for H if every two different elements (edges and vertices) of H are distinguished by at least one vertex of Wm...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1859714 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849684723692994560 |
|---|---|
| author | Bao-Hua Xing Sunny Kumar Sharma Vijay Kumar Bhat Hassan Raza Jia-Bao Liu |
| author_facet | Bao-Hua Xing Sunny Kumar Sharma Vijay Kumar Bhat Hassan Raza Jia-Bao Liu |
| author_sort | Bao-Hua Xing |
| collection | DOAJ |
| description | A vertex w∈VH distinguishes (or resolves) two elements (edges or vertices) a,z∈VH∪EH if dw,a≠dw,z. A set Wm of vertices in a nontrivial connected graph H is said to be a mixed resolving set for H if every two different elements (edges and vertices) of H are distinguished by at least one vertex of Wm. The mixed resolving set with minimum cardinality in H is called the mixed metric dimension (vertex-edge resolvability) of H and denoted by m dimH. The aim of this research is to determine the mixed metric dimension of some wheel graph subdivisions. We specifically analyze and compare the mixed metric, edge metric, and metric dimensions of the graphs obtained after the wheel graphs’ spoke, cycle, and barycentric subdivisions. We also prove that the mixed resolving sets for some of these graphs are independent. |
| format | Article |
| id | doaj-art-c072f3f33c884845b33ab43832b8bc83 |
| institution | DOAJ |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c072f3f33c884845b33ab43832b8bc832025-08-20T03:23:23ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/18597141859714The Vertex-Edge Resolvability of Some Wheel-Related GraphsBao-Hua Xing0Sunny Kumar Sharma1Vijay Kumar Bhat2Hassan Raza3Jia-Bao Liu4School of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaSchool of Mathematics, Faculty of Sciences, Shri Mata Vaishno Devi University, Katra 182320, Jammu and Kashmir, IndiaSchool of Mathematics, Faculty of Sciences, Shri Mata Vaishno Devi University, Katra 182320, Jammu and Kashmir, IndiaBusiness School, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaA vertex w∈VH distinguishes (or resolves) two elements (edges or vertices) a,z∈VH∪EH if dw,a≠dw,z. A set Wm of vertices in a nontrivial connected graph H is said to be a mixed resolving set for H if every two different elements (edges and vertices) of H are distinguished by at least one vertex of Wm. The mixed resolving set with minimum cardinality in H is called the mixed metric dimension (vertex-edge resolvability) of H and denoted by m dimH. The aim of this research is to determine the mixed metric dimension of some wheel graph subdivisions. We specifically analyze and compare the mixed metric, edge metric, and metric dimensions of the graphs obtained after the wheel graphs’ spoke, cycle, and barycentric subdivisions. We also prove that the mixed resolving sets for some of these graphs are independent.http://dx.doi.org/10.1155/2021/1859714 |
| spellingShingle | Bao-Hua Xing Sunny Kumar Sharma Vijay Kumar Bhat Hassan Raza Jia-Bao Liu The Vertex-Edge Resolvability of Some Wheel-Related Graphs Journal of Mathematics |
| title | The Vertex-Edge Resolvability of Some Wheel-Related Graphs |
| title_full | The Vertex-Edge Resolvability of Some Wheel-Related Graphs |
| title_fullStr | The Vertex-Edge Resolvability of Some Wheel-Related Graphs |
| title_full_unstemmed | The Vertex-Edge Resolvability of Some Wheel-Related Graphs |
| title_short | The Vertex-Edge Resolvability of Some Wheel-Related Graphs |
| title_sort | vertex edge resolvability of some wheel related graphs |
| url | http://dx.doi.org/10.1155/2021/1859714 |
| work_keys_str_mv | AT baohuaxing thevertexedgeresolvabilityofsomewheelrelatedgraphs AT sunnykumarsharma thevertexedgeresolvabilityofsomewheelrelatedgraphs AT vijaykumarbhat thevertexedgeresolvabilityofsomewheelrelatedgraphs AT hassanraza thevertexedgeresolvabilityofsomewheelrelatedgraphs AT jiabaoliu thevertexedgeresolvabilityofsomewheelrelatedgraphs AT baohuaxing vertexedgeresolvabilityofsomewheelrelatedgraphs AT sunnykumarsharma vertexedgeresolvabilityofsomewheelrelatedgraphs AT vijaykumarbhat vertexedgeresolvabilityofsomewheelrelatedgraphs AT hassanraza vertexedgeresolvabilityofsomewheelrelatedgraphs AT jiabaoliu vertexedgeresolvabilityofsomewheelrelatedgraphs |