Wiener polarity index and related molecular topological descriptors of titanium oxide nanotubes

The relations between the physico-chemical properties of a chemical compounds its molecular structure properties are used in quantitative structure activity and property relationship studies by using graph-theoretical techniques. The Wiener polarity index is the number of unordered pairs of vertices lying at distance 3 in a graph. This index is correlated to the cluster coefficient of chemical networks. The Wiener polarity index has been used to exhibit quantitative structure–property relationships in a series of acyclic and cycle-containing hydrocarbons. In this paper, we consider three variants of the graph of titanium oxide TiO₂, that is, two-dimensional lattice, nanotubes and nanotorus. For all these graphs, we compute the number of pairs of vertices lying at distance one, two and three. Using this information, we compute the Wiener polarity index and leap Zagreb indices of these graphs.