Wiener polarity index and related molecular topological descriptors of titanium oxide nanotubes. Issue 11 (19th February 2021) - Imran, Muhammad; Malik, Mehar Ali; Javed, Ramsha
Abstract: 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. Abstract : The information about the number of atoms lying at second and third distance from a given atom help in obtaining the leap Zagreb indices and Wiener po larity index of a molecule. These indices have previ ously shown potential for their applications in QSAR and QSPR studies. The cardinalities of first, second and third neighborhoods of any atom in TiO2 nanotubes, nanotorus and their 2D lattices are characterized. The vertices lying at distance one, two and three form the vertex ν can be observed by green, blue and red colors.