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

Alaa Altassan, Muhammad Imran () and Shehnaz Akhter
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Alaa Altassan: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Muhammad Imran: Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates
Shehnaz Akhter: School of Natural Sciences, National University of Sciences and Technology, Islamabad 44000, Pakistan

Mathematics, 2022, vol. 10, issue 16, 1-13

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.

Keywords: graph operations; distance; eccentricity; eccentric distance sum polynomial (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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