The Metric Dimension of Subdivisions of Lilly Graph, Tadpole Graph and Special Trees

Consider a robot that is navigating in space represented by graph and wants to know its current location. It can send signal find out how far it from each set of fixed landmarks. We study the problem computing minimum number landmarks required, where they should be placed so always determine The nodes are located called metric basis graph, dimension graph. On other hand, G smallest size B vertices distinguish vertex pair shortest-path distance some B. finding an arbitrary NP-complete problem. Also, has several applications different areas, such as geographical routing protocols, network discovery verification, pattern recognition, image processing, combinatorial optimization. In this paper, we subdivisions graphs, including Lilly Tadpole special trees star tree, bistar coconut tree.