On certain topological indices of graphs

TL;DR

This paper establishes new bounds for various topological indices of graphs, including irregularity, degree variance, and Zagreb indices, and introduces an upper bound for graph energy using the IRB-index, based on Laplacian spectral radius.

Contribution

It provides novel bounds for multiple vertex- and edge-based topological indices and introduces an upper bound for graph energy through the IRB-index, leveraging Laplacian spectral properties.

Findings

New bounds for Albertson irregularity index and degree variance index.

A new upper bound for graph energy using IRB-index.

Results rely on Laplacian spectral radius characterization.

Abstract

In this paper we give new bounds for a several vertex-based and edge-based topological indices of graphs: Albertson irregularity index, degree variance index, Mostar and the first Zagreb index. Moreover, we give a new upper bound for the energy of graphs through IRB-index. Most of our results rely on a well-known characterization of the Laplacian spectral radius.