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Notes on the Localization of Generalized Hexagonal Cellular Networks

Author

Listed:
  • Muhammad Azeem

    (Department of Mathematics, Riphah International University Lahore, Lahore 54000, Pakistan)

  • Muhammad Kamran Jamil

    (Department of Mathematics, Riphah International University Lahore, Lahore 54000, Pakistan)

  • Yilun Shang

    (Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK)

Abstract

The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined and proved the exact locating number for this network. Furthermore, in this technique, each node of a generalized hexagonal cellular network can be accessed uniquely. Lastly, we also discussed the generalized version of the locating set and locating number.

Suggested Citation

  • Muhammad Azeem & Muhammad Kamran Jamil & Yilun Shang, 2023. "Notes on the Localization of Generalized Hexagonal Cellular Networks," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:844-:d:1060432
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    References listed on IDEAS

    as
    1. András Sebő & Eric Tannier, 2004. "On Metric Generators of Graphs," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 383-393, May.
    2. Raza, Hassan & Hayat, Sakander & Pan, Xiang-Feng, 2018. "On the fault-tolerant metric dimension of convex polytopes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 172-185.
    3. Laxman Saha & Rupen Lama & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2022. "Fault-Tolerant Metric Dimension of Circulant Graphs," Mathematics, MDPI, vol. 10(1), pages 1-16, January.
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