On the Atom Bond Connectivity Index of Titania Nanotubes TiO2 (m, n)
Molecular graph
Titania Carbon Nanotubes TiO2(m
n)
Orthogonal cuts
atom-bond connectivity index
Let G(V,E) be a simple molecular graph, for a graph G(V,E) with vertex(atom) set V and the edge(bond) set E, the third version of atom bond connectivity index is defined as 
where mv is the number of edges of G lying near to u than to v. In this research paper, we compute the third version of atomic-bond connectivity index of the Titania Nanotubes TiO2(m,n).