Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks

Ali H. Alkhaldi, Muhammad Kamran Aslam, Muhammad Javaid and Abdulaziz Mohammed Alanazi
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Ali H. Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha P.O. Box 9004, Saudi Arabia
Muhammad Kamran Aslam: Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, Pakistan
Muhammad Javaid: Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, Pakistan
Abdulaziz Mohammed Alanazi: Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2021, vol. 9, issue 12, 1-18

Abstract: 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.

Keywords: connected networks; metric dimension; fractional metric dimension; resolving neighbourhoods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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