Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 Geometric-arithmetic index-energy predicting the physical properties of alkanes 1013 1032 14879 10.22049/cco.2024.28999.1807 EN Bilal Ahmad Rather Department of Mathematics, Samarkand International University of Technology, Samarkand 140100, Uzbekistan M. Aouchiche Polytechnique Montreal, Montreal, QC, Canada M. Imran Department of Mathematical and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia S. Mondal RISE, MASEP Group, University of Sharjah, Sharjah 27272, UAE Journal Article 2023 09 18 The topological indices play a crucial role in generating the weighted adjacency matrix, which exhibits significant diversity from both theoretical and application perspectives compared to the ordinary adjacency matrix. One such notable weighted matrix is the geometric-arithmetic matrix, generated from the well-known $GA$ (geometric-arithmetic) index. Here, we focus on a comparative study of the $GA$ index and the geometric-arithmetic energy $\mathcal{GAE}$. We establish several tight bounds on $\mathcal{GAE}$ involving various graph invariants and identify the corresponding extremal graphs. Additionally, we compare the correlation of the molecular property Bp (boiling point) with $GA$ and $\mathcal{GAE}$. Our findings reveal that the Bp shows good correlation with $\mathcal{GAE}$ than with $GA$ index. Furthermore, we examine the role of $\mathcal{GAE}$ in explaining different properties of drugs associated with kidney disease. https://comb-opt.azaruniv.ac.ir/article_14879_5d98d961611894f82bff67df74dc99ac.pdf