Vertex PI_v Topological Index of Titania Carbon Nanotubes TiO₂(m,n)

A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Padmakar-Ivan (PI) index of a graph G is defined as PI(G) = Σ_e=uv∈E(G) [n_u + n_v], where n_u is the number of edges of G lying closer to v than u, analogously n_v. In this paper, we compute the vertex PI index of Titania carbon Nanotubes TiO₂[m,n].