# Fifth Geometric--Arithmetic Index VS Atom--Bond Connectivity Index and Heat of Formation

## TL;DR

This paper explores the correlation between the fifth geometric--arithmetic index and other topological indices, demonstrating its potential in predicting heat of formation for hydrocarbons.

## Contribution

It introduces the analysis of the fifth geometric--arithmetic index's predictive power, especially its strong correlation with the atom--bond connectivity index and heat of formation.

## Key findings

- Strong correlation with atom--bond connectivity index for hydrocarbons
- Good correlation with heat of formation
- Potential for improved molecular property prediction

## Abstract

The geometric--arithmetic indices are widely considered in the chemical graph theory in the last decade. The reason of introducing new indices is to gain prediction of target properties of considered molecules that is better than the prediction obtained by already known indices. In the case of the fifth geometric--arithmetic index hitherto no ability of prediction of some molecule property has been considered. In this paper we investigate correlations between the fifth geometric--arithmetic index and some other degree--based topological indices on the family of octane isomers and polyaromatic hydrocarbons. Since a very good correlation is established with the well known atom--bond connectivity index for polyaromatic hydrocarbons and then for the alkane series, the relation between the heat of formation and the fifth geometric--arithmetic index is examined and a good correlation is confirmed in that case as well.