The Wiener polarity index of benzenoid systems and nanotubes

In this paper, we consider a molecular descriptor called the Wiener polarity index, which is defined as the number of unordered pairs of vertices at distance three in a graph. Molecular descriptors play a fundamental role in chemistry, materials engineering, and in drug design since they can be correlated with a large number of physico-chemical properties of molecules. As the main result, we develop a method for computing the Wiener polarity index for two basic and most commonly studied families of molecular graphs, benzenoid systems and carbon nanotubes. The obtained method is then used to find a closed formula for the Wiener polarity index of any benzenoid system. Moreover, we also compute this index for zig-zag and armchair nanotubes

ON CERTAIN TOPOLOGICAL INDICES OF BENZENOID COMPOUNDS

Drug discovery is mainly the result of chance discovery and massive screening of large corporate libraries of synthesized or naturally-occurring compounds. Computer aided drug design is an approach to rational drug design made possible by the recent advances in computational chemistry in various fields of chemistry, such as molecular graphics, molecular mechanics, quantum chemistry, molecular dynamics, library searching, prediction of physical, chemical, and biological properties.  The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. Topological indices are designed basically by transforming a molecular graph into a number. A topological index is a numeric quantity of a molecule that is mathematically derived from the structural graph of a molecule. In this paper we compute certain topological indices of pyrene molecular graph. The topological indices are used in quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) studies.Â

The Vertex Version of Weighted Wiener Number for Bicyclic Molecular Structures

Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. We call such a graph, which is derived from a chemical compound, a molecular graph. Evidence shows that the vertex-weighted Wiener number, which is defined over this molecular graph, is strongly correlated to both the melting point and boiling point of the compounds. In this paper, we report the extremal vertex-weighted Wiener number of bicyclic molecular graph in terms of molecular structural analysis and graph transformations. The promising prospects of the application for the chemical and pharmacy engineering are illustrated by theoretical results achieved in this paper