Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 1 2024 03 01 Extremal Kragujevac trees with respect to Sombor indices 177 183 14503 10.22049/cco.2023.28058.1430 EN Tsend-Ayush Selenge Department of Mathematics, National University of Mongolia, P.O.Box 187/46A, Ulaanbaatar, Mongolia Batmend Horoldagva Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia 0000-0003-3417-2612 Journal Article 2022 10 29 The concept of the Sombor indices of a graph was introduced by Gutman. A vertex-edge variant of the Sombor index of graphs is called the KG-Sombor index.  Recently, the Sombor and  KG-Sombor indices of Kragujevac trees were studied, and the extremal Kragujevac trees with respect to these indices were empirically  determined.   Here we give analytical proof of the results. https://comb-opt.azaruniv.ac.ir/article_14503_1e960bffbe2d564ae0c9dfb41bec1299.pdf