Metric Dimension of r-th power of paths

Abstract: For a simple connected graph G = (V,E), an ordered set W ⊆V , is calleda resolving set of G if for every pair of two distinct vertices uand v, there is anelement win Wsuch that d(u,w) ≠ d(v,w). A metric basis of G is a resolving setof G with minimum cardinality. The metric dimension of G is the cardinality ofa metric basis and it is denoted by β(G). In this article, we determine the metricdimension of any power of finite paths.

Keywords: Code, Resolving set, Metric dimension.