On path related graphs with constant metric dimension

Abstract

Let G is a connected graph. A set of vertices W resolves a graph G, if every vertex is uniquely determined by its coordinate of distances to the vertices in W. The minimum cardinality of resolving set G is called the metric dimension of G. In this paper, we show that the graphs P ² _n, P ³ _n, M(P _n) and T(P _n) have constant metric dimension.