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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ali H. Alkhaldi & Muhammad Kamran Aslam & Muhammad Javaid & Abdulaziz Mohammed Alanazi, 2021. "Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1383-:d:575108
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