On Eccentricity-Based Topological Indices and Polynomials of Phosphorus-Containing Dendrimers

Kang, Shin Min; Iqbal, Zahid; Ishaq, Muhammad; Sarfraz, Rabia; Aslam, Adnan; Nazeer, Waqas

doi:10.3390/sym10070237

Cited by 29 publications

(8 citation statements)

References 19 publications

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“…Thereby, the computation of TIs is one of the flourishing lines of research. The significance of the above-mentioned indices in formulating mathematical models for various biological activities can be seen in [14,17,[48][49][50][51][52][53]. In the next section, we compute these eccentricity-based indices for a PolyEThyleneAmidoAmine (PETAA) dendrimer.…”

Section: Methodsmentioning

confidence: 99%

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

et al. 2019

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Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

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Section: Methodsmentioning

confidence: 99%

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

et al. 2019

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“…These dendrimers have been functionalized with pendant nitroxyl radicals, and these radicals show a strong magnetic exchange interaction. Some topological aspects of this dendrimer are discussed in [44]. Let D 1 (n) be the molecular graph of this dendrimers, where n represents the generation stage of D 1 (n).…”

Section: Phosphorus-containing Dendrimersmentioning

confidence: 99%

On Irregularity Measures of Some Dendrimers Structures

et al. 2019

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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.

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“…In this work, we are interested in the irregularity indices of the molecular graphs of different types of dendrimers. For some topological aspects of different complex dendrimers structures, we refer the interested reader to [29][30][31][32][33][34][35][36][37]. We will restrict our attention to three dendrimers Polyamidoamine (PAMAM), Poly(EThyleneAmidoAmine) (PETAA), and poly(PropylETherIMine)(PETIM) 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 Eccentricity-Based Topological Indices and Polynomials of Phosphorus-Containing Dendrimers

Cited by 29 publications

References 19 publications

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

On Irregularity Measures of Some Dendrimers Structures

Comparison of Irregularity Indices of Several Dendrimers Structures

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