University of Isfahan Transactions on Combinatorics 2251-8657 14 3 2024 09 03 On relationship between reformulated Sombor and other vertex--degree indices 197 209 28728 10.22108/toc.2024.136304.2036 EN Emina I. Milovanovic Faculty of Electronic Engineering, University of Niš, Niš, Serbia Stefan Stankov Faculty of Electronic Engineering, University of Niš, Niš, Serbia Şerife Burcu Bozkurt Altındağ Department of Mathematics, Faculty of Science, Selçuk University, Konya, Turkey Marjan Matejic Faculty of Electronic Engineering, University of Nis, Serbia Igor Z. Milovanovic Faculty of Electronic Engineering, University of Niš, Niš, Serbia Journal Article 2023 01 02 Let $G=(V,E)$, $V=\{v_1, v_2,\ldots,v_n\}$, $E=\{e_1, e_2,\ldots,e_m\}$, be a simple connected graph with $n\ge 2$ vertices and $m$ edges, with vertex degree sequence $\Delta=d_1\ge d_2\ge \cdots \ge d_n=\delta$, $ d_i=d(v_i)$, and edge degree sequence $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots \ge d(e_n)=\delta_e$. The reformulated Sombor index is defined as $RS(G) =\sum_{e_i\sim e_j}\sqrt{d(e_i)^2+d(e_j)^2}$. We consider a relationship between reformulated Sombor index and some of the vertex--degree-based indices. https://toc.ui.ac.ir/article_28728_33cf749a9f637f268ea9d91e11e339b3.pdf