On Irregularity Measures of Some Dendrimers Structures

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

doi:10.3390/math7030271

Cited by 25 publications

(16 citation statements)

References 36 publications

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“…Recently authors computed irregularity indices of a nanotube [47]. Recently Gao et al computed irregularity measures of some dendrimer structures in [48] and molecular structures in [49]. Actually, the authors computed only four irregularity measures for some classes of dendrimers in [48].…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

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Imbalance-Based Irregularity Molecular Descriptors of Nanostar Dendrimers

et al. 2019

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Dendrimers are branched organic macromolecules with successive layers of branch units surrounding a central core. The molecular topology and the irregularity of their structure plays a central role in determining structural properties like enthalpy and entropy. Irregularity indices which are based on the imbalance of edges are determined for the molecular graphs associated with some general classes of dendrimers. We also provide graphical analysis of these indices for the above said classes of dendrimers.

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Section: Preliminaries and Notationsmentioning

confidence: 99%

“…Recently Gao et al computed irregularity measures of some dendrimer structures in [48] and molecular structures in [49]. Actually, the authors computed only four irregularity measures for some classes of dendrimers in [48]. These structures are used as long infinite chain macromolecules in chemistry and related areas.…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Imbalance-Based Irregularity Molecular Descriptors of Nanostar Dendrimers

et al. 2019

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“…Although plenty of studies have been executed on the distance-based and degree-based indices of molecular graphs, the analyses of irregularity measures for chemical structures still need attention. In [4,16,22,32], the irregularity measures of various chemical structures were investigated.…”

Section: Introductionmentioning

confidence: 99%

The measure of irregularities of nanosheets

et al. 2020

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Nanosheets are two-dimensional polymeric materials, which are among the most active areas of investigation of chemistry and physics. Many diverse physicochemical properties of compounds are closely related to their underlying molecular topological descriptors. Thus, topological indices are fascinating beginning points to any statistical approach for attaining quantitative structure–activity (QSAR) and quantitative structure–property (QSPR) relationship studies. Irregularity measures are generally used for quantitative characterization of the topological structure of non-regular graphs. In various applications and problems in material engineering and chemistry, it is valuable to be well-informed of the irregularity of a molecular structure. Furthermore, the estimation of the irregularity of graphs is helpful for not only QSAR/QSPR studies but also different physical and chemical properties, including boiling and melting points, enthalpy of vaporization, entropy, toxicity, and resistance. In this article, we compute the irregularity measures of graphene nanosheet, H-naphtalenic nanosheet, {\text{SiO}}_{2} nanosheet, and the nanosheet covered by {C}_{3} and {C}_{6}.

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“…Although 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. In [25][26][27][28], the irregularity measures of various chemical structures were investigated. In this work, we are interested in the irregularity indices of the molecular graphs of different types of dendrimers.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Irregularity Indices of Several Dendrimers Structures

et al. 2019

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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.

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On Irregularity Measures of Some Dendrimers Structures

Cited by 25 publications

References 36 publications

Imbalance-Based Irregularity Molecular Descriptors of Nanostar Dendrimers

Imbalance-Based Irregularity Molecular Descriptors of Nanostar Dendrimers

The measure of irregularities of nanosheets

Comparison of Irregularity Indices of Several Dendrimers Structures

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