Computing entire Zagreb indices of some dendrimer structures

Wei Gao,Muhammad Ishaq,Zahid Iqbal,Adnan Aslam,Muhammad Aamir,Abdul Jaleel

doi:10.1515/mgmc-2020-0027

Abstract

Abstract Topological indices are numerical numbers associated to molecular graphs and are invariant of a graph. In QSAR/QSPR study, Zagreb indices are used to explain the different properties of chemical compounds at the molecular level mathematically. They have been studied extensively due to their ease of calculation and numerous applications in place of the existing chemical methods which needed more time and increased the costs. In this paper, we compute precise values of new versions of Zagreb indices for two classes of dendrimers.

Highlights

Dendrimers are discrete nanostructures with the welldefined, homogeneous and monodisperse structure having tree-like arms with low polydispersity and high functionality
The vertices correspond to atoms and the edges correspond to chemical bonds between the atoms
Many topological indices have been introduced based on the transformation of a molecular graph into a number that examines the relationship between the structure, properties, and activity of chemical compounds in molecular modelling

Summary

Introduction

Dendrimers are discrete nanostructures with the welldefined, homogeneous and monodisperse structure having tree-like arms with low polydispersity and high functionality. Many topological indices have been introduced based on the transformation of a molecular graph into a number that examines the relationship between the structure, properties, and activity of chemical compounds in molecular modelling. These topological indices are invariant under graph isomorphism, If A and B are two molecular graphs such that A ≅ B, we have Top(A) = Top(B), where Top(A) and Top(B) denote the topological indices of A and B, respectively. The first and second Zagreb index of a molecular graph G are denoted and defined as: These formulas were obtained analyzing the structural dependency of total π electron energy.

The entire Zagreb indices for molecular graph of Trizane based dendrimer

Conclusion