University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 16 2 2025 06 01 A Note on the Additively Weighted Mostar Index of Graphs 155 170 114912 10.22052/ijmc.2024.255424.1899 EN Liju Alex Bishop Chulaparambil Memorial College‎, ‎Kottayam-686001‎, ‎India ‎Gopalapillai Indulal Department of Mathematics‎, ‎St.Aloysius College‎, ‎Edathua‎, ‎Alappuzha‎ -689573, ‎India Joyamol T Baby Bishop Chulaparambil Memorial College‎, ‎Kottayam-686001‎, ‎India Journal Article 2024 09 08 ‎In this article‎, ‎we discuss the additively weighted Mostar index‎, ‎an innovative topological measure that extends the traditional Mostar index by incorporating edge weights computed as the sum of the degrees of their end point vertices‎. ‎We focus on its application within the set $\mathcal{U}_n$ comprising all unicyclic graphs of order $n$‎. ‎Our study rigorously establishes the first two sharp lower and upper bounds for this index across graphs in $\mathcal{U}_n$‎. ‎Additionally‎, ‎we analyze the additively weighted Mostar index of Cartesian product graphs and investigate its properties across various graph classes‎. ‎Furthermore‎, ‎we demonstrate the practical utility of this index by comparing its effectiveness against eight other distance-based topological indices in predicting chemical properties of octane isomers‎. ‎Remarkably‎, ‎we find that the additively weighted Mostar index outperforms or matches the predictive capabilities of other indices in linear models with these chemical properties‎, ‎highlighting its potential in quantitative structure-property relationships‎. ‎This research significantly contributes to both graph theory and chemical informatics by showcasing the unique advantages of the additively weighted Mostar index in structural analysis and predictive modeling‎. https://ijmc.kashanu.ac.ir/article_114912_dfcd53d40bd7d6b7b75c56502fa209f1.pdf