On the Characterization of a Minimal Resolving Set for Power of Paths
Laxman Saha, Mithun Basak, Kalishankar Tiwary, Kinkar Chandra Das, Yilun Shang · Mathematics · 2022
For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w). A metric basis of G is a resolving set of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis and it is denoted by β(G). In this article, we determine the metric dimension of power of finite paths and characterize all metric bases for the same.