Local Metric Resolvability of Generalized Petersen Graphs

Rashad Ismail (), Asim Nadeem and Kamran Azhar
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Rashad Ismail: Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha 61421, Saudi Arabia
Asim Nadeem: Department of Mathematics, Forman Christian College, Lahore 54600, Pakistan
Kamran Azhar: Department of Mathematics, Forman Christian College, Lahore 54600, Pakistan

Mathematics, 2024, vol. 12, issue 14, 1-14

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.

Keywords: generalized Petersen graphs; metric dimension; local metric dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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