On Neighbourhood Zagreb index of product graphs

TL;DR

This paper introduces the Neighbourhood Zagreb index, a new topological measure, and derives explicit formulas for it in various product graphs, demonstrating its relevance to chemical structures and nanomaterials.

Contribution

The paper presents a novel topological index, the Neighbourhood Zagreb index, and provides explicit formulas for product graphs, linking graph theory to chemical and nanostructure analysis.

Findings

Explicit formulas for the index on Cartesian, Tensor, and Wreath product graphs.

Application of the index to chemically important graphs and nanostructures.

Establishment of the index's relevance to chemical properties and molecular structures.

Abstract

There is powerful relation between the chemical behaviour of chemical compounds and their molecular structures. Topological indices defined on these chemical molecular structures are capable to predict physical properties, chemical reactivity and biological activity. In this article, a new topological index named as Neighbourhood Zagreb index $(M_N)$ is presented. Here the chemical importance of this newly introduced index is studied and some explicit results for this index of different product graphs such as Cartesian, Tensor and Wreath product is derived. Some of these results are applied to obtain the Neighbourhood Zagreb index of several chemically important graphs and nano-structures.