On independent resolving number of TiO ₂ [ m , n ] nanotubes

Let G ( V , E ) be a Graph. A set W ⊆ V of vertices resolves a graph G if every vertex of G is uniquely determined by its vector of distances to the vertices in W . The metric dimension of G is the minimum cardinality of a resolving set. By imposing different conditions on W we get conditional resolving sets. A resolving set W is said to be an independent resolving set if W contains isolated vertices. Independent resolving number denoted by i r (G) is referred to its cardinality. In this paper we investigate independent resolving number for Titanium dioxide Nanotube.