ABSTRACT:
Numerous studies indicate that drug properties like boiling point, melting point, pKa value etc., indicate that there is a strong relationship between chemical characteristics of chemical compounds and drugs and their molecular structures. In the fields of chemical graph theory, molecular topology and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological descriptors are derived from hydrogen – suppressed molecular graphs, in which the atoms are represented by vertices and the bonds by edges. The connections between the atoms can be described by various types of topological matrices like a distance or adjacency matrix, which can be mathematically manipulated so as to derive a single number, usually known as graph invariant, graph – theoretical index or topological index. Smaller the size of the matrix, the easier is the computation and hence better the runtime of the algorithms developed. This presentation aims to introduce a technique to determine the Wiener polarity index of a tree from its subtree, which aids in reducing the size of the distance matrix used for calculating the Wiener polarity index and hence reduces the computational complexity.