Local Metric Resolvability of Generalized Petersen Graphs

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.