Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 05 12 Degree-weighted Sombor indices of trees and unicyclic graphs: An extremal approach 14945 10.22049/cco.2025.30315.2413 EN Nasrin Dehgardi Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran Tomislav Došlić University of Zagreb, Faculty of Civil Engineering, Zagreb, Croatia Journal Article 2025 01 28 ‎We consider two generalizations of the Sombor index, obtained by weighting the standard contribution $\sqrt{d_\Omega(\eta)^2+d_\Omega(\eta')^2}$ of an edge $\eta\eta'$ of a graph $\Omega$ by the sum and by the product of degrees of its end-vertices, respectively. The first generalization has been considered under the name of the elliptic Sombor index, while the second one seems to be new. We consider trees and unicyclic graphs on a given number of vertices $n$ with a given maximum degree $\Delta $ and characterize the graphs minimizing both generalizations over those classes of graphs. Sombor index‎ ‎degree-weighted Sombor index‎ ‎elliptic Sombor‎ ‎index‎ ‎trees‎ ‎unicyclic graphs‎ https://comb-opt.azaruniv.ac.ir/article_14945_b169f34b8997421eeb45d99b6950e961.pdf