Affiliation:
1. Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha 61421, Saudi Arabia
2. 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.
Funder
the Deanship of Scientific Research at King 205 Khalid University for funding this work through large group Research Project
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