Exploring the Edge Hyper-Zagreb Index of Graphs: Applications and Predictions of Thermodynamic Properties for Organic Linear Acenes Molecules

TL;DR

This paper investigates the edge hyper-Zagreb index of graphs, especially for organic linear Acenes molecules, and uses it to predict thermodynamic properties through topological indices.

Contribution

It introduces calculations of the edge hyper-Zagreb index for graph operations and applies topological indices to predict properties of Acenes molecules.

Findings

Derived formulas for the edge hyper-Zagreb index of graph products and joins.

Established correlations between topological indices and thermodynamic properties.

Predicted properties like electron affinity and heat of formation for Acenes molecules.

Abstract

The paper discusses the edge hyper-Zagreb index of a graph, which is calculated by replacing vertex degrees with edge degrees. The degree of an edge is determined by adding up the degrees of the end vertices of the edge and subtracting 2. We examine the edge hyper-Zagreb index of the Cartesian product and join of graphs, and also calculate it for organic linear Acenes molecules with the formula (C4n+2H2n+4). We establish a correlation between topological indices based on the number of rings and predict thermodynamic properties of Acenes family, such as electron affinity, bond, heat of formation and gap energy, using the Topological Indices Method (T IM).