Use of vertex index in structure-activity analysis and design of molecules

The last few decades have witnessed application of graph theory and topological indices derived from molecular graph in structure-activity analysis. Such applications are based on regression and various multivariate analyses. Most of the topological indices are computed for the whole molecule and used as descriptors for explaining properties/activities of chemical compounds. However, some substructural descriptors in the form of topological distance based vertex indices have been found to be useful in identifying activity related substructures and in predicting pharmacological and toxicological activities of bioactive compounds. Another important aspect of drug discovery e.g. designing novel pharmaceutical candidates could also be done from the distance distribution associated with such vertex indices. In this article, we will review the development and applications of this approach both in activity prediction as well as in designing novel compounds.