On relationship between reformulated Sombor and other vertex--degree indices

Abstract

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.