Abstract
Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are σ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index.
Highlights
The rapid growth in the field of medicine has resulted in the production of unknown nanomaterials, crystalline materials, and drugs
The PAMAM dendrimers are a family of dendrimers which is made of repetitively branched subunits of amide and amine functionality
A modern trend in quantitative structure-activity relationship (QSAR)/quantitative structure-property relationship (QSPR) studies is the use of properties which can be secure from the molecular structure without any other input data
Summary
The rapid growth in the field of medicine has resulted in the production of unknown nanomaterials, crystalline materials, and drugs. The linear growth in the size of dendrimers makes them the ideal delivery vehicle candidates for the study of effects of composition, and size of polymer in the biological properties like cytotoxicity, blood plasma retention time, lipid bilayer interactions, and filtration, see [21] and references therein. These molecules were first discovered (and studied) by E.Buhleier [22], D. Plenty of work has been executed on the distance and degree based indices of molecular graphs, the analyses of irregularity measures for chemical structures still need attention. We will restrict our attention to three dendrimers Polyamidoamine (PAMAM), Poly(EThyleneAmidoAmine) (PETAA), and poly(PropylETherIMine)(PETIM) dendrimers
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