Distance-Based Fractional Dimension of Certain Wheel Networks
Metric dimension is one of the distance-based parameters which are used to find the position of the robot in a network space by utilizing lesser number of notes and minimum consumption of time. It is also used to characterize the chemical compounds. The metric dimension has a wide range of applicati...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/8870335 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559577751617536 |
|---|---|
| author | Hassan Zafar Muhammad Javaid Mamo Abebe Ashebo |
| author_facet | Hassan Zafar Muhammad Javaid Mamo Abebe Ashebo |
| author_sort | Hassan Zafar |
| collection | DOAJ |
| description | Metric dimension is one of the distance-based parameters which are used to find the position of the robot in a network space by utilizing lesser number of notes and minimum consumption of time. It is also used to characterize the chemical compounds. The metric dimension has a wide range of applications in the field of computer science such as integer programming, radar tracking, pattern recognition, robot navigation, and image processing. A vertex x in a network W resolves the adjacent pair of vertices uv if x attains an unequal distance from end points of uv. A local resolving neighbourhood set RLuv is a set of vertices of W which resolve uv. A mapping α:VW⟶0,1 is called local resolving function of W if αRLuv≥1 for any adjacent pair of vertices of uv of W and the minimal value of αRLuv for all local resolving functions α of W is called local fractional metric dimension of W. In this paper, we have studied the local fractional metric dimension of wheel-related networks such as web-wheel network, subdivision of wheel network, line network of subdivision of wheel network, and double-wheel network and also examined their boundedness. |
| format | Article |
| id | doaj-art-b59ead72c8564804a7ce12b54377d95e |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b59ead72c8564804a7ce12b54377d95e2025-02-03T01:29:42ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/8870335Distance-Based Fractional Dimension of Certain Wheel NetworksHassan Zafar0Muhammad Javaid1Mamo Abebe Ashebo2Department of MathematicsDepartment of MathematicsDepartment of MathematicsMetric dimension is one of the distance-based parameters which are used to find the position of the robot in a network space by utilizing lesser number of notes and minimum consumption of time. It is also used to characterize the chemical compounds. The metric dimension has a wide range of applications in the field of computer science such as integer programming, radar tracking, pattern recognition, robot navigation, and image processing. A vertex x in a network W resolves the adjacent pair of vertices uv if x attains an unequal distance from end points of uv. A local resolving neighbourhood set RLuv is a set of vertices of W which resolve uv. A mapping α:VW⟶0,1 is called local resolving function of W if αRLuv≥1 for any adjacent pair of vertices of uv of W and the minimal value of αRLuv for all local resolving functions α of W is called local fractional metric dimension of W. In this paper, we have studied the local fractional metric dimension of wheel-related networks such as web-wheel network, subdivision of wheel network, line network of subdivision of wheel network, and double-wheel network and also examined their boundedness.http://dx.doi.org/10.1155/2024/8870335 |
| spellingShingle | Hassan Zafar Muhammad Javaid Mamo Abebe Ashebo Distance-Based Fractional Dimension of Certain Wheel Networks Journal of Mathematics |
| title | Distance-Based Fractional Dimension of Certain Wheel Networks |
| title_full | Distance-Based Fractional Dimension of Certain Wheel Networks |
| title_fullStr | Distance-Based Fractional Dimension of Certain Wheel Networks |
| title_full_unstemmed | Distance-Based Fractional Dimension of Certain Wheel Networks |
| title_short | Distance-Based Fractional Dimension of Certain Wheel Networks |
| title_sort | distance based fractional dimension of certain wheel networks |
| url | http://dx.doi.org/10.1155/2024/8870335 |
| work_keys_str_mv | AT hassanzafar distancebasedfractionaldimensionofcertainwheelnetworks AT muhammadjavaid distancebasedfractionaldimensionofcertainwheelnetworks AT mamoabebeashebo distancebasedfractionaldimensionofcertainwheelnetworks |