Augmented Zagreb Index of Polyhex Nanotubes

TL;DR

This paper derives explicit formulas for the augmented Zagreb index, a topological measure, specifically applied to arm-chair and zigzag polyhex nanotubes, enhancing understanding of their structural properties.

Contribution

It provides the first closed-form expressions for the augmented Zagreb index of specific polyhex nanotube structures, advancing topological analysis in nanomaterials.

Findings

Closed formulas for arm-chair polyhex nanotubes

Closed formulas for zigzag polyhex nanotubes

Enhanced understanding of nanotube topological properties

Abstract

Augmented Zagreb Index is a newly defined degree based topological invariant which has been well established for its better correlation properties and is defined as $AZI(G)= \sum_{uv\in E(G)}(\frac{d_G (u)d_G (v)}{d_G (u)+ d_G (v)-2})^3 $, where $E(G)$ is the edge set of graph $G$ and $d(u),\,\,d(v)$ are the degrees of the end vertices $u$ and $v$ of edge $uv$, respectively. It has outperformed many well known degree based topological indices. In this article we give closed formulae for the augmented Zagreb index of arm-chair polyhex and zigzag edge polyhex nanotubes.