On Irregularity Measures of Some Dendrimers Structures

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

doi:10.3390/math7030271

Abstract

A graph is said to be a regular graph if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of non-regular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? Furthermore, evaluations of the irregularity of underline molecular graphs could be valuable for QSAR/QSPR studies, and for the expressive determines of chemical and physical properties, such as enthalpy of vaporization, toxicity, resistance, Entropy, melting and boiling points. In this paper, we think over the following four irregularity measures: the irregularity index by Albertson, σ irregularity index, the total irregularity index and the variance of vertex degrees. By way of graph structural estimation and derivations, we determine these irregularity measures of the molecular graphs of different classes of dendrimers.

Highlights

Nanotechnology is a modern and fast-growing field that requires the design, production, and exploitation of structures at the nanoscale
Badetti et al [43] synthesized five novel generations of phosphorus dendrimers based on a cyclotriphosphazene core with stable TEMPO radicals end groups
These dendrimers have been functionalized with pendant nitroxyl radicals, and these radicals show a strong magnetic exchange interaction

Summary

Introduction

Nanotechnology is a modern and fast-growing field that requires the design, production, and exploitation of structures at the nanoscale. Dendrimers are nano-sized, radially symmetric molecules with the very well homogeneous and monodisperse structure containing tree-like arms [2,3,4,5]. Dendrimers are recognised by unusual properties like small size, high functionality, cavities, well-defined three-dimensional structure, and globular shape. These properties make them rare candidates for using in nanotechnology and diverse biomedical applications [6,7]. Dendrimers are inviting the interest of a great number of scientists because of their wide range of talented applications in various fields such as material, nanoscience, biology, medicine, physics [8,9,10,11,12,13,14,15]

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Conclusion