The Eccentric-Distance Sum Polynomials of Graphs by Using Graph Products

Abstract

The correlations between the physico-chemical properties of a chemical structure and its molecular structure-properties are used in quantitative structure-activity and property relationship studies (QSAR/QSPR) by using graph-theoretical analysis and techniques. It is well known that some structure-activity and quantitative structure-property studies, using eccentric distance sum, are better than the corresponding values obtained by using the Wiener index. In this article, we give precise expressions for the eccentric distance sum polynomial of some graph products such as join, Cartesian, lexicographic, corona and generalized hierarchical products. We implement our outcomes to calculate this polynomial for some significant families of molecular graphs in the form of the above graph products.