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Local Metric Resolvability of Generalized Petersen Graphs

Author

Listed:
  • Rashad Ismail

    (Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha 61421, Saudi Arabia
    These authors contributed equally to this work.)

  • Asim Nadeem

    (Department of Mathematics, Forman Christian College, Lahore 54600, Pakistan
    These authors contributed equally to this work.)

  • Kamran Azhar

    (Department of Mathematics, Forman Christian College, Lahore 54600, Pakistan)

Abstract

The local metric basis and local metric generator can play a significant role in deciding optimal locations for many facilities like hospitals, fire stations, medical labs, and grocery stores. The local metric basis generates codes in terms of distance for each node of the graph in such a way that no two adjacent nodes have the same code, which allows for the optimal allocation of resources. In the current manuscript, the local metric basis (LMB) for three families of graphs, P ( n , 1 ) , P ( n , 2 ) , and P ( n , 3 ) , which are generalized Petersen graphs and commonly employed in interconnection networks, are determined. The manuscript also proposes an algorithm to compute the local metric basis and its application in the optimal placement of different facilities in a region.

Suggested Citation

  • Rashad Ismail & Asim Nadeem & Kamran Azhar, 2024. "Local Metric Resolvability of Generalized Petersen Graphs," Mathematics, MDPI, vol. 12(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2179-:d:1433383
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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. Kelenc, Aleksander & Kuziak, Dorota & Taranenko, Andrej & G. Yero, Ismael, 2017. "Mixed metric dimension of graphs," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 429-438.
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