M-polynomial and topological indices of zigzag edge coronoid fused by starphene

Afzal, Farkhanda; Hussain, Sabir; Afzal, Deeba; Hameed, Saira

doi:10.1515/chem-2020-0161

Cited by 23 publications

(13 citation statements)

References 20 publications

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“…After simplifying above, we get the desired result (2). Proof Let T F (μ) be the Cayley tree dendrimer for p iterations.…”

Section: Corollary 4 the Modified First Neighborhood Index Of Tmentioning

confidence: 88%

“…Munir et al [ 52 ] evaluated degree-based indices of titania nanotube from M-polynomial. Recently, M-polynomials of some nano-structures and zigzag edge coronoid fused by starphene are derived in [ 2 , 57 ]. Topological descriptors for the crystal structure of titanium difluoride are obtained in [ 34 ].…”

Section: Introductionmentioning

confidence: 99%

“…When α = −1, −2, − 1 2 , we have neighborhood inverse degree index (N I D), modified first neighborhood index ( m N M 1 ) and neighborhood zeroth order index (N Z), respectively which are formulated by Kulli [27] as follows: Forgotten topological index (F(Γ )) [13] ω Γ (x) 2 + ω Γ (y) 2 Inverse sum indeg index (I SI (Γ )) [ Table 2 Formulation of molecular descriptors based on neighborhood degree sum of nodes for a graph Γ…”

Section: Introductionmentioning

confidence: 99%

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Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers

Mondal

De²,

Pal

2021

Eur. Phys. J. Plus

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Topological index is a connection between the chemical structure and the real number that remains invariant under graph isomorphism. In structure–property and structure–activity modeling, topological indices are considered as essential molecular descriptors to predict different physicochemical properties of molecule. Dendrimers are considered to be the most significant, commercially accessible basic components in nanotechnology. In this report, some neighborhood degree sum-based molecular descriptors are obtained for the fractal tree and the Cayley tree dendrimers. Neighborhood M-polynomial yields a family of topological indices for a molecular graph in less time compared to the usual computation from their definitions. Some indices are obtained using neighborhood M-polynomial approach. In addition, some multiplicative neighborhood degree sum-based molecular descriptors are evaluated for fractal and Cayley tree dendrimers. The graphical representations of the outcomes are presented. A comparative study of the findings with some well-known degree-based indices is performed. Usefulness of the descriptors in modeling different properties and activities is discussed.

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“…After simplifying above, we get the desired result (2). Proof Let T F (μ) be the Cayley tree dendrimer for p iterations.…”

Section: Corollary 4 the Modified First Neighborhood Index Of Tmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers

Mondal

De²,

Pal

2021

Eur. Phys. J. Plus

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“…We refer to [40] for the mathematical analysis of coronoid and related structures. The new research effort [41] is for polynomial investigation of hollow coronoid. In this paper, the authors computed several polynomials.…”

Section: Construction Of Hollow Coronoidmentioning

confidence: 99%

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

et al. 2021

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Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

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“…Some indices are calculated by Munir et al ( 2016 ). In the past, Kang et al ( 2018 ), Afzal et al ( 2020a , b ), Cancan et al ( 2020a , b ), and Khalaf et al ( 2020 ) used these formulas to compute topological indices via M-polynomial and a lot of work has been done in this area. One more set of nine topological indices has been computed by Afzal et al ( 2020c ).…”

Section: M-polynomialmentioning

confidence: 99%

Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube

Shin

Hussain

Afzal³

et al. 2021

Front. Chem.

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In this article, we provide new formulas to compute the reduced reciprocal randić index, Arithmetic geometric1 index, SK index, SK1 index, SK2 index, edge version of the first zagreb index, sum connectivity index, general sum connectivity index, and the forgotten index using the M-polynomial and finding these topological indices for a boron triangular nanotube. We also elaborate the results with graphical representations.

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M-polynomial and topological indices of zigzag edge coronoid fused by starphene

Cited by 23 publications

References 20 publications

Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers

Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers

Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube

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