Comparison of Irregularity Indices of Several Dendrimers Structures

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.

Mostar indices of SiO2 nanostructures and melem chain nanostructures

“…Hence, the computation and estimation of topological descriptors of molecular structures are progressive trends of research, which have special significance in nanotechnology and theoretical chemistry. The interested reader is referred to refs [26,34–44] for a detailed study of this subject. In our calculations, we apply the cut method, which was introduced in ref.…”

The Topological Aspects of Phthalocyanines and Porphyrins Dendrimers

“…The evaluation and analysis of topological indices of molecular structures are modern trends of research, which are of the significant importance in nanotechnology and theoretical chemistry. We refer the interested reader to [22]- [24], [30], [31], [35]- [37], [39], [40], [54] for an introduction to this subject. We use the cut method that was suggested in [42] and they used it to find the Wiener index of graphs.…”

On Face Index of Silicon Carbides

“…Several researchers have studied different aspects and applications of the TIs. For contents related to studies on lower/upper bounds maxima/ minima of TIs, see [1][2][3][4][5], studies on chemistry and drugs see [6][7][8][9][10], and other applications, see [11][12][13]. Another vital contribution of the study of the TIs is their effectiveness in studying the different aspects of new drugs and chemical compounds, which is an immense need of the medical science and industry.…”