New results on the Diminished Sombor index

Abstract

The diminished Sombor index of a simple graph [Formula: see text] is defined by [Formula: see text] where [Formula: see text] and [Formula: see text] denote the degrees of the vertices [Formula: see text] and [Formula: see text], respectively. In this paper, we study the diminished Sombor index and develop a suite of sharp inequalities connecting it to standard graph parameters (order, size, minimum/maximum degree) and classical degree-based indices.