Molecular Properties of Symmetrical Networks Using Topological Polynomials

AbstractA numeric quantity that comprehend characteristics of molecular graph Γ of chemical compound is known as topological index. This number is, in fact, invariant with respect to symmetry properties of molecular graph Γ. Many researchers have established, after diverse studies, a parallel between the physico chemical properties like boiling point, stability, similarity, chirality and melting point of chemical species and corresponding chemical graph. These descriptors defined on chemical graphs are extremely helpful for researchers to conduct regression model like QSAR/QSPR and better understand the physical features, complexity of molecules, chemical and biological properties of underlying compound.In this paper, several structure descriptors of vital importance, namely, first, second, modified and augmented Zagreb indices, inverse and general Randic indices, symmetric division, harmonic, inverse sum and forgotten indices of Hex-derived Meshes (networks) of two kinds, namely, HDN1(n) and HDN2(n) are computed and recovered using general approach of topological polynomials.

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On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽

10.3390/sym10080320 ◽

2018 ◽

Vol 10 (8) ◽

pp. 320 ◽

Cited By ~ 12

Author(s):

Young Kwun ◽

Abaid Virk ◽

Waqas Nazeer ◽

M. Rehman ◽

Shin Kang

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Compound ◽

Zagreb Indices ◽

Silicon Carbon ◽

Physico Chemical ◽

Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

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Computing SS Index of Certain Dendrimers

Journal of Mathematics ◽

10.1155/2021/7483508 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Weidong Zhao ◽

M.C. Shanmukha ◽

A. Usha ◽

Mohammad Reza Farahani ◽

K.C. Shilpa

Keyword(s):

Chemical Structure ◽

Topological Index ◽

Chemical Compounds ◽

Biological Properties ◽

Molar Refraction ◽

Topological Indices ◽

Zagreb Indices ◽

Mathematical Properties ◽

Chemical Graph Theory ◽

Physico Chemical

The numerical descriptor gathers the data from the molecular graphs and helps to know the characteristics of the chemical structure known as topological index. The QSAR/QSPR/QSTR studies are benefited with the significant role played by topological indices in the drug design. Topological indices provide the information about the physical/chemical/biological properties of chemical compounds. The Zagreb indices are widely studied because of their extensive usage in chemical graph theory. Inspired by the earlier work on inverse sum indeg index (ISI index), novel topological index known as SS index is introduced and computed for four dendrimer structures. Also, the strong correlation coefficient between SS index and 5 physico-chemical characteristics such as boiling point (bp), molar volume (mv), molar refraction (mr), heats of vaporization (hv), and critical pressure (cp) of 67 alkane isomers have been determined. It is found that newly introduced index has shown good correlation in comparison with three most popular existing indices (ISI index and first and second Zagreb indices). In the last part, the mathematical properties of SS index are discussed.

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Choosing the exponent in the definition of the connectivity index

Journal of the Serbian Chemical Society ◽

10.2298/jsc0109605g ◽

2001 ◽

Vol 66 (9) ◽

pp. 605-611 ◽

Cited By ~ 13

Author(s):

Ivan Gutman ◽

Mirko Lepovic

Keyword(s):

Carbon Atom ◽

Topological Index ◽

Organic Molecules ◽

Molecular Graph ◽

Chemical Properties ◽

Connectivity Index ◽

Physico Chemical ◽

Definition Of ◽

Molecular Branching ◽

Suitable Measure

Let ?v denote the degree of the vertex v of a molecular graph G. Then the connectivity index of G is defined as C (?) = G (?,C) = ? (?u?v)?, where the summation goes over all pairs of adjacent vertices. The exponent ? is usually chosen to be equal to -1/2, but other options were considered as well, especially ?=-1. We show that whereas C(-1/2) is a suitable measure of branching of the carbon-atom skeleton of organic molecules, and thus applicable as a topological index for modeling physico-chemical properties of the respective compounds, this is not the case with C(-1). The value of ? is established, beyond which C(?) fails to correctly reflect molecular branching.

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On Some Properties of Multiplicative Topological Indices in Silicon-Carbon

Journal of Mathematics ◽

10.1155/2021/4611199 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Abid Mahboob ◽

Sajid Mahboob ◽

Mohammed M. M. Jaradat ◽

Nigait Nigar ◽

Imran Siddique

Keyword(s):

Graph Theory ◽

Structural Properties ◽

Topological Index ◽

Molecular Graph ◽

Chemical Compounds ◽

Google Maps ◽

Chemical Graph ◽

Zagreb Indices ◽

Silicon Carbon ◽

Connectivity Indices

The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( M 1 G and ( M 1 G )), generalized multiplicative geometric arithmetic index ( GA α II G ), and multiplicative sum connectivity and multiplicative product connectivity indices ( SCII G and PCII G ) of SiC 4 − I m , n and SiC 4 − II m , n .

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On the Certain Topological Indices of Titania Nanotube TiO2[m, n]

Zeitschrift für Naturforschung A ◽

10.1515/zna-2017-0101 ◽

2017 ◽

Vol 72 (7) ◽

pp. 647-654 ◽

Cited By ~ 2

Author(s):

M. Javaid ◽

Jia-Bao Liu ◽

M. A. Rehman ◽

Shaohui Wang

Keyword(s):

Chemical Compound ◽

Topological Index ◽

Molecular Graph ◽

Topological Indices ◽

Zagreb Index ◽

Zagreb Indices ◽

Mathematical Expressions ◽

Titania Nanotube ◽

Physical Features ◽

Atom Bond

AbstractA numeric quantity that characterises the whole structure of a molecular graph is called the topological index that predicts the physical features, chemical reactivities, and boiling activities of the involved chemical compound in the molecular graph. In this article, we give new mathematical expressions for the multiple Zagreb indices, the generalised Zagreb index, the fourth version of atom-bond connectivity (ABC4) index, and the fifth version of geometric-arithmetic (GA5) index of TiO2[m, n]. In addition, we compute the latest developed topological index called by Sanskruti index. At the end, a comparison is also included to estimate the efficiency of the computed indices. Our results extended some known conclusions.

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Graph Neural Networks for Prediction of Fuel Ignition Quality

10.26434/chemrxiv.12280325.v1 ◽

2020 ◽

Author(s):

Artur Schweidtmann ◽

Jan Rittig ◽

Andrea König ◽

Martin Grohe ◽

Alexander Mitsos ◽

...

Keyword(s):

Neural Networks ◽

Octane Number ◽

Molecular Graph ◽

Chemical Properties ◽

Graph Representation ◽

Structure Property ◽

Oxygenated Hydrocarbons ◽

Physico Chemical ◽

Ignition Quality ◽

Graph Neural Networks

<div>Prediction of combustion-related properties of (oxygenated) hydrocarbons is an important and challenging task for which quantitative structure-property relationship (QSPR) models are frequently employed. Recently, a machine learning method, graph neural networks (GNNs), has shown promising results for the prediction of structure-property relationships. GNNs utilize a graph representation of molecules, where atoms correspond to nodes and bonds to edges containing information about the molecular structure. More specifically, GNNs learn physico-chemical properties as a function of the molecular graph in a supervised learning setup using a backpropagation algorithm. This end-to-end learning approach eliminates the need for selection of molecular descriptors or structural groups, as it learns optimal fingerprints through graph convolutions and maps the fingerprints to the physico-chemical properties by deep learning. We develop GNN models for predicting three fuel ignition quality indicators, i.e., the derived cetane number (DCN), the research octane number (RON), and the motor octane number (MON), of oxygenated and non-oxygenated hydrocarbons. In light of limited experimental data in the order of hundreds, we propose a combination of multi-task learning, transfer learning, and ensemble learning. The results show competitive performance of the proposed GNN approach compared to state-of-the-art QSPR models making it a promising field for future research. The prediction tool is available via a web front-end at www.avt.rwth-aachen.de/gnn.</div>

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Chitosan-Nanocellulose Composites for Regenerative Medicine Applications

Current Medicinal Chemistry ◽

10.2174/0929867327666200127152834 ◽

2020 ◽

Vol 27 (28) ◽

pp. 4584-4592 ◽

Cited By ~ 2

Author(s):

Avik Khan ◽

Baobin Wang ◽

Yonghao Ni

Keyword(s):

Regenerative Medicine ◽

Preparation Method ◽

Chemical Properties ◽

Biological Properties ◽

Next Generation ◽

Structure Property ◽

Physico Chemical ◽

Structure Property Relationship ◽

Attractive Candidate ◽

Fundamental Understanding

Regenerative medicine represents an emerging multidisciplinary field that brings together engineering methods and complexity of life sciences into a unified fundamental understanding of structure-property relationship in micro/nano environment to develop the next generation of scaffolds and hydrogels to restore or improve tissue functions. Chitosan has several unique physico-chemical properties that make it a highly desirable polysaccharide for various applications such as, biomedical, food, nutraceutical, agriculture, packaging, coating, etc. However, the utilization of chitosan in regenerative medicine is often limited due to its inadequate mechanical, barrier and thermal properties. Cellulosic nanomaterials (CNs), owing to their exceptional mechanical strength, ease of chemical modification, biocompatibility and favorable interaction with chitosan, represent an attractive candidate for the fabrication of chitosan/ CNs scaffolds and hydrogels. The unique mechanical and biological properties of the chitosan/CNs bio-nanocomposite make them a material of choice for the development of next generation bio-scaffolds and hydrogels for regenerative medicine applications. In this review, we have summarized the preparation method, mechanical properties, morphology, cytotoxicity/ biocompatibility of chitosan/CNs nanocomposites for regenerative medicine applications, which comprises tissue engineering and wound dressing applications.

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Computing Topological Indices for Para-Line Graphs of Anthracene

Open Chemistry ◽

10.1515/chem-2019-0093 ◽

2019 ◽

Vol 17 (1) ◽

pp. 955-962 ◽

Cited By ~ 1

Author(s):

Zhiqiang Zhang ◽

Zeshan Saleem Mufti ◽

Muhammad Faisal Nadeem ◽

Zaheer Ahmad ◽

Muhammad Kamran Siddiqui ◽

...

Keyword(s):

Graph Theory ◽

Chemical Compound ◽

Line Graph ◽

Molecular Graph ◽

Chemical Properties ◽

Molar Refraction ◽

Chromatographic Behavior ◽

Chemical Graph ◽

Chemical Graph Theory ◽

And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

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On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

10.20944/preprints201806.0066.v1 ◽

2018 ◽

Author(s):

Young Chel Kwun ◽

Abaid ur Rehman Virk ◽

Waqas Nazeer ◽

Shin Min Kang

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Compound ◽

Silicon Carbon ◽

Physico Chemical ◽

Structure Research

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q].

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