Metric-based resolvability of polycyclic aromatic hydrocarbons

Azeem, Muhammad; Nadeem, Muhammad Faisal

doi:10.1140/epjp/s13360-021-01399-8

Cited by 80 publications

(39 citation statements)

References 37 publications

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“…The coronene and circumcoronene are the second and third family members of polycyclic aromatic hydrocarbons for the specific values of k = 2, 3 respectively. The resolvability parameters of this rich family of polycyclic aromatic hydrocarbons are studied in [41]. We will extend this work for the quartz structure shown in the Fig.…”

Section: Definition 16mentioning

confidence: 88%

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Metric-Based Resolvability of Quartz Structure

Singla¹,

Al‐Wesabi²,

Pathania³

et al. 2022

Computers, Materials &Amp; Continua

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Silica has three major varieties of crystalline. Quartz is the main and abundant ingredient in the crust of our earth. While other varieties are formed by the heating of quartz. Silica quartz is a rich chemical structure containing enormous properties. Any chemical network or structure can be transformed into a graph, where atoms become vertices and the bonds are converted to edges, between vertices. This makes a complex network easy to visualize to work on it. There are many concepts to work on chemical structures in terms of graph theory but the resolvability parameters of a graph are quite advance and applicable topic. Resolvability parameters of a graph is a way to getting a graph into unique form, like each vertex or edge has a unique identification by means of some selected vertices, which depends on the distance of vertices and its pattern in a particular graph. We have dealt some resolvability parameters of SiO 2 quartz. We computed the resolving set for quartz structure and its variants, wherein we proved that all the variants of resolvability parameters of quartz structures are constant and do not depend on the order of the graph.

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Section: Definition 16mentioning

confidence: 88%

“…Another structure of VC 5 C 7 nanotubes is reshaped with this parameter and is available in [40]. The recent studies of all these parameters are available in [41].…”

Section: Introductionmentioning

confidence: 99%

Metric-Based Resolvability of Quartz Structure

Singla¹,

Al‐Wesabi²,

Pathania³

et al. 2022

Computers, Materials &Amp; Continua

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“…The bounds of partitioning on the specific type of nanotube are studied in [39]. All the resolvability parameters of graph theory on the polycyclic aromatic hydrocarbons are discussed in [2]. For the fault-tolerant concept discussed in [21] for basic graphs, [34] for different interconnection networks along with implementation of its applications, some recent work can be acquired by the references [35], [36], [41].…”

Section: Introductionmentioning

confidence: 99%

Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid

et al. 2021

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Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons. The mathematical study of chemicals is of great interest to different specialties researchers. While graph theory always played a significant role to make chemical structures understandable and blessed with applications also. After transforming the chemical structure into a graph, one can implement different theoretical and implicative studies on structures. Metric dimension is considered as one of the most studied and implicative parameters of graph theory. In this concept, few suggested vertices are chosen such as the remaining vertices have unique locations or identifications. In this study, we discussed different metric-based parameters for the hollow coronoid structure. INDEX TERMS Hollow coronoid; metric dimension; resolving set; fault-tolerant metric dimension.

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“…Moving towards the edge metric dimension, barycentric subdivision of Cayley graph studied in [22], few work on the convex polytopes structure discussed by [23,24], the wheel graphs related chemical structures are discussed in [25] and a quantitative review between metric its other versions is done in [26], moreover, the seminal work on the edge metric dimension can be found in [27]. The renowned chemical topology of polycyclic aromatic hydrocarbons are discussed in [28], with the conceptualization of resolvability parameters.…”

Section: Introductionmentioning

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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Metric-based resolvability of polycyclic aromatic hydrocarbons

Cited by 80 publications

References 37 publications

Metric-Based Resolvability of Quartz Structure

Metric-Based Resolvability of Quartz Structure

Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid

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

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