A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal–Organic Framework

Ghani, Muhammad Usman; Sultan, Faisal; Eldin, Sayed M.; Khan, Abdul Rauf; Liu, Jia‐Bao; Cancan, Murat

doi:10.3390/molecules27206975

Cited by 27 publications

(15 citation statements)

References 23 publications

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“…TDA is a collection of tools originating from topology and geometry, designed to provide qualitative and quantitative descriptors of structures in data sets. They have been successfully applied to various systems in different fields ranging from cosmology , to solid state physics. − Topological measures such as the Randić and Zagreb indices rest on the topological properties of graphs, making them particularly interesting when a physical system has natural graph representation, such as molecular compounds. Similarly, statistics of knots provides relevant insight on configurations of elongated objects such as DNA or proteins .…”

Section: Resultsmentioning

confidence: 99%

“…On the other hand, topology has been used to provide insight on physicochemical properties of matter, hinting at potential alternative ways to quantify disorder. Examples of the application of topology include computing graph invariant indices such as the Randić index and Zagreb indices, measuring statistics of knots , and rings, , or using persistent homology. , In particular, topological defects are a key element to understand the melting of crystals in 2D into a hexatic phase, by losing translational order, and a fluid phase, by losing orientational order, within KTHNY theory. − …”

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confidence: 99%

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Topological Learning for the Classification of Disorder: An Application to the Design of Metasurfaces

Madeleine,

Podoliak,

Buchnev

et al. 2023

ACS Nano

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Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods or explicitly designed and built lithographically. For example, correlated disorder, induced by a minimum inter-nanostructure distance or by hyperuniformity properties, is particularly beneficial for light extraction. Inspired by topology, we introduce numerical descriptors to provide quantitative measures of disorder with universal properties, suitable to treat both uncorrelated and correlated disorder at all length scales. The accuracy of these topological descriptors is illustrated both theoretically and experimentally by using them to design plasmonic metasurfaces with controlled disorder that we then correlate to the strength of their surface lattice resonances. These descriptors are an example of topological tools that can be used for the fast and accurate design of disordered structures or as aid in improving their fabrication methods.

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Topological Learning for the Classification of Disorder: An Application to the Design of Metasurfaces

Madeleine,

Podoliak,

Buchnev

et al. 2023

ACS Nano

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“…Manzoor et al in [ 26 ] and Ghani et al in [ 27 ] recently offered another strategy that is a little bit novel in the literature: applying the idea of Shannon’s entropy [ 28 ] in terms of topological indices. The following formula represents the valency-based entropy:

where

represents the atoms,

represents the edge set, and

represents the edge weight of edge

.…”

Section: Definitions Of Entropies Via K -Banhatti ...mentioning

confidence: 99%

“…Here, we calculate the first K-hyper Banhatti entropy of CNB n using Table 1 and Equation (27) in Equation ( 9) as described below:…”

Section: Entropy Related To the First K-hyper Banhatti Index Of Cn B Nmentioning

confidence: 99%

Entropy Related to K-Banhatti Indices via Valency Based on the Presence of C6H6 in Various Molecules

et al. 2023

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Entropy is a measure of a system’s molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon’s entropy metric is applied to represent a random graph’s variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules’ chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at K-Banhatti entropies using K-Banhatti indices for C6H6 embedded in different chemical networks. Our goal is to investigate the valency-based molecular invariants and K-Banhatti entropies for three chemical networks: the circumnaphthalene (CNBn), the honeycomb (HBn), and the pyrene (PYn). In order to reach conclusions, we apply the method of atom-bond partitioning based on valences, which is an application of spectral graph theory. We obtain the precise values of the first K-Banhatti entropy, the second K-Banhatti entropy, the first hyper K-Banhatti entropy, and the second hyper K-Banhatti entropy for the three chemical networks in the main results and conclusion.

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“…This study fills the gap in the current framework since the neighborhood degree descriptors and M-polynomial function have several applications, including the measurement of the acentric factor, the calculation of enthalpy and the determination of heat capacity to mention a few [ 28 ]. Additionally, this work has been expanded by applying Shannon’s entropy model to calculate the Entropy using these descriptors [ 29 , 30 , 31 ]. Moreover, a comparison of the two variants of these nanosheets has also been carried out using various graphing tools.…”

Section: Introductionmentioning

confidence: 99%

Comparative Study of Molecular Descriptors of Pent-Heptagonal Nanostructures Using Neighborhood M-Polynomial Approach

Xavier¹,

Ghani

Imran

et al. 2023

Molecules

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In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet C5C7(a,b) is presented. The conjugated molecules follow the graph spectral theory, in terms of bonding, non-bonding and antibonding Ruckel molecular orbitals. They are demonstrated to be immediately determinable from their topological characteristics. The effort of chemical and pharmaceutical researchers is significantly increased by the need to conduct numerous chemical experiments to ascertain the chemical characteristics of such a wide variety of novel chemicals. In order to generate novel cellular imaging techniques and to accomplish the regulation of certain cellular mechanisms, scientists have utilized the attributes of nanosheets such as their flexibility and simplicity of modification, out of which carbon nanosheets stand out for their remarkable strength, chemical stability, and electrical conductivity. With efficient tools like polynomials and functions that can forecast compound features, mathematical chemistry has a lot to offer. One such approach is the M-polynomial, a fundamental polynomial that can generate a significant number of degree-based topological indices. Among them, the neighborhood M-polynomial is useful in retrieving neighborhood degree sum-based topological indices that can help in carrying out physical, chemical, and biological experiments. This paper formulates the unique M-polynomial approach which is used to derive and compare a variety of neighborhood degree-based molecular descriptors and the corresponding entropy measures of two variations of pent-heptagonal carbon nanosheets. Furthermore, a regression analysis on these descriptors has also been carried out which can further help in the prediction of various properties of the molecule.

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A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal–Organic Framework

Cited by 27 publications

References 23 publications

Topological Learning for the Classification of Disorder: An Application to the Design of Metasurfaces

Topological Learning for the Classification of Disorder: An Application to the Design of Metasurfaces

Entropy Related to K-Banhatti Indices via Valency Based on the Presence of C6H6 in Various Molecules

Comparative Study of Molecular Descriptors of Pent-Heptagonal Nanostructures Using Neighborhood M-Polynomial Approach

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