New boundes for Sombor index of Graphs

TL;DR

This paper establishes new bounds for the Sombor index of graphs using various mathematical inequalities and indices, providing estimates and error intervals to understand its accuracy limits.

Contribution

It introduces novel bounds for the Sombor index based on multiple indices and inequalities, enhancing the understanding of its possible values.

Findings

Derived bounds using triangle inequality and other indices.

Provided error intervals for the Sombor index estimates.

Enhanced accuracy understanding of the Sombor index in graph theory.

Abstract

In this paper, we find some bounds for the Sombor index of the graph G by triangle inequality, arithmetic index, geometric index, forgotten index (F(G)), arithmetic-geometric (AG) index, geometric-arithmetic (GA) index, symmetric division deg index (SDD(G)) and some central and dispersion indices. The bounds could state estimated values and error intervals of the Sombor index to show limits of accuracy. The error intervals are written as inequalities.