Majorization under constraints and bounds of the second Zagreb index

TL;DR

This paper develops a theoretical framework for majorization under constraints to establish bounds on the second Zagreb index of graphs, improving existing results through analytical and numerical methods.

Contribution

It introduces a novel majorization analysis for subsets of ^n and applies it to derive tighter bounds for the second Zagreb index of graphs.

Findings

Derived new bounds for the second Zagreb index

Improved upon existing bounds in the literature

Validated results with theoretical and numerical examples

Abstract

In this paper we present a theoretical analysis in order to establish maximal and minimal vectors with respect to the majorization order of particular subsets of \Re ^n: Afterwards we apply these issues to the calcula- tion of bounds for a topological descriptor of a graph known as the second Zagreb index. Finally, we show how our bounds may improve the re- sults obtained in the literature, providing some theoretical and numerical examples.