Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks
Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local frac...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1383 |
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| author | Ali H. Alkhaldi Muhammad Kamran Aslam Muhammad Javaid Abdulaziz Mohammed Alanazi |
| author_facet | Ali H. Alkhaldi Muhammad Kamran Aslam Muhammad Javaid Abdulaziz Mohammed Alanazi |
| author_sort | Ali H. Alkhaldi |
| collection | DOAJ |
| description | Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots. |
| first_indexed | 2024-03-10T10:24:55Z |
| format | Article |
| id | doaj.art-f54afdc0a6e34259ac226ee79bf7f69e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:24:55Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f54afdc0a6e34259ac226ee79bf7f69e2023-11-22T00:09:12ZengMDPI AGMathematics2227-73902021-06-01912138310.3390/math9121383Bounds of Fractional Metric Dimension and Applications with Grid-Related NetworksAli H. Alkhaldi0Muhammad Kamran Aslam1Muhammad Javaid2Abdulaziz Mohammed Alanazi3Department of Mathematics, College of Science, King Khalid University, Abha P.O. Box 9004, Saudi ArabiaDepartment of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi ArabiaMetric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.https://www.mdpi.com/2227-7390/9/12/1383connected networksmetric dimensionfractional metric dimensionresolving neighbourhoods |
| spellingShingle | Ali H. Alkhaldi Muhammad Kamran Aslam Muhammad Javaid Abdulaziz Mohammed Alanazi Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks Mathematics connected networks metric dimension fractional metric dimension resolving neighbourhoods |
| title | Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks |
| title_full | Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks |
| title_fullStr | Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks |
| title_full_unstemmed | Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks |
| title_short | Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks |
| title_sort | bounds of fractional metric dimension and applications with grid related networks |
| topic | connected networks metric dimension fractional metric dimension resolving neighbourhoods |
| url | https://www.mdpi.com/2227-7390/9/12/1383 |
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