Local metric and partition resolvability of graphs with applications

The distance-based graph parameters are being used extensively in the fields of chemistry, computer science, scheduling and in many operations’ management problems. The unique identification of vertices plays a key role in the computation of these parameters. The local versions of these parameters deal with adjacent vertices and, in this manner, provide more applicability. In this manuscript, the exact values of local metric dimension and local partition dimension of tadpole and necklace graphs have been computed. The article also discusses the application of a local metric basis in the optimal allocation of fire stations in a region.