scholarly journals Some Bounds on Bond Incident Degree Indices with Some Parameters

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Muhammad Rizwan ◽  
Akhlaq Ahmad Bhatti ◽  
Muhammad Javaid ◽  
Fahd Jarad
Keyword(s):  
Partition Coefficient ◽  
Polyaromatic Hydrocarbons ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Molar Refraction ◽  
Quantitative Structure ◽  
Structure Property ◽  
Acentric Factor ◽  
Zagreb Index ◽  
Water Partition Coefficient

It is considered that there is a fascinating issue in theoretical chemistry to predict the physicochemical and structural properties of the chemical compounds in the molecular graphs. These properties of chemical compounds (boiling points, melting points, molar refraction, acentric factor, octanol-water partition coefficient, and motor octane number) are modeled by topological indices which are more applicable and well-used graph-theoretic tools for the studies of quantitative structure-property relationships (QSPRs) and quantitative structure-activity relationships (QSARs) in the subject of cheminformatics. The π -electron energy of a molecular graph was calculated by adding squares of degrees (valencies) of its vertices (nodes). This computational result, afterwards, was named the first Zagreb index, and in the field of molecular graph theory, it turned out to be a well-swotted topological index. In 2011, Vukicevic introduced the variable sum exdeg index which is famous for predicting the octanol-water partition coefficient of certain chemical compounds such as octane isomers, polyaromatic hydrocarbons (PAH), polychlorobiphenyls (PCB), and phenethylamines (Phenet). In this paper, we characterized the conjugated trees and conjugated unicyclic graphs for variable sum exdeg index in different intervals of real numbers. We also investigated the maximum value of SEIa for bicyclic graphs depending on a > 1 .

scholarly journals Topological indices of rhombus type silicate and oxide networks

2017 ◽  
Vol 95 (2) ◽  
pp. 134-143 ◽  
Author(s):  
M. Javaid ◽  
Masood Ur Rehman ◽  
Jinde Cao
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Activity ◽  
Structure Property Relationship ◽  
Cartesian Coordinate ◽  
Atom Bond

For a molecular graph, a numeric quantity that characterizes the whole structure of a graph is called a topological index. In the studies of quantitative structure – activity relationship (QSAR) and quantitative structure – property relationship (QSPR), topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we compute general Randić, first general Zagreb, generalized Zagreb, multiplicative Zagreb, atom-bond connectivity (ABC), and geometric arithmetic (GA) indices for the rhombus silicate and rhombus oxide networks. In addition, we also compute the latest developed topological indices such as the fourth version of ABC (ABC4), the fifth version of GA (GA5), augmented Zagreb, and Sanskruti indices for the foresaid networks. At the end, a comparison between all the indices is included, and the result is shown with the help of a Cartesian coordinate system.

scholarly journals Chemical Graph Theory for Property Modeling in QSAR and QSPR—Charming QSAR & QSPR

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 60
Author(s):  
Paulo C. S. Costa ◽  
Joel S. Evangelista ◽  
Igor Leal ◽  
Paulo C. M. L. Miranda
Keyword(s):  
Graph Theory ◽  
Learning Strategies ◽  
Molecular Graph ◽  
Three Dimensional ◽  
Chemical Compounds ◽  
Biological Properties ◽  
Theory Approach ◽  
Quantitative Structure ◽  
Structure Property ◽  
Molecular Fragments

Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR) are mathematical models for the prediction of the chemical, physical or biological properties of chemical compounds. Usually, they are based on structural (grounded on fragment contribution) or calculated (centered on QSAR three-dimensional (QSAR-3D) or chemical descriptors) parameters. Hereby, we describe a Graph Theory approach for generating and mining molecular fragments to be used in QSAR or QSPR modeling based exclusively on fragment contributions. Merging of Molecular Graph Theory, Simplified Molecular Input Line Entry Specification (SMILES) notation, and the connection table data allows a precise way to differentiate and count the molecular fragments. Machine learning strategies generated models with outstanding root mean square error (RMSE) and R2 values. We also present the software Charming QSAR & QSPR, written in Python, for the property prediction of chemical compounds while using this approach.

scholarly journals On multiplicative degree based topological indices for planar octahedron networks

2020 ◽  
Vol 43 (1) ◽  
pp. 219-228
Author(s):  
Ghulam Dustigeer ◽  
Haidar Ali ◽  
Muhammad Imran Khan ◽  
Yu-Ming Chu
Keyword(s):  
Graph Theory ◽  
Information Science ◽  
Biological Activities ◽  
Molecular Graph ◽  
Triangular Prism ◽  
Structure Property ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Chemical Graph Theory ◽  
Analytical Formulas

AbstractChemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is at least one connection between its vertices. The number that describes the topology of the graph is called the topological index. Cheminformatics is a new subject which is a combination of chemistry, mathematics and information science. It studies quantitative structure-activity (QSAR) and structure-property (QSPR) relationships that are used to predict the biological activities and properties of chemical compounds. We evaluated the second multiplicative Zagreb index, first and second universal Zagreb indices, first and second hyper Zagreb indices, sum and product connectivity indices for the planar octahedron network, triangular prism network, hex planar octahedron network, and give these indices closed analytical formulas.

scholarly journals The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

2021 ◽  
pp. 54-75
Author(s):  
Mohammed Alsharafi ◽  
Yusuf Zeren ◽  
Abdu Alameri
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Strong Product ◽  
Chemical Graph Theory ◽  
Mathematical Operations

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

QSPR Study on n-Octanol/Water Partition Coefficient of PCDD/Fs by Three-Dimensional Holographic Vector of Atomic Interaction Field

2011 ◽  
Vol 356-360 ◽  
pp. 83-88 ◽  
Author(s):  
Shu Qiao ◽  
Kun Xie ◽  
Chuan Fu ◽  
Jie Pan
Keyword(s):  
Partition Coefficient ◽  
Organic Pollutants ◽  
Three Dimensional ◽  
Qsar Model ◽  
Atomic Interaction ◽  
Structure Property ◽  
Qspr Model ◽  
Chemical Structures ◽  
Interaction Field ◽  
Water Partition Coefficient

Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) are a group of important persistent organic pollutants. Quantitative structure–property relationship (QSPR) modeling is a powerful approach for predicting the properties of environmental organic pollutants from their structure descriptors. In this study, a QSPR model is established for estimating n-octanol/water partition coefficient (log KOW) of PCDD/Fs. Three-dimensional holographic vector of atomic interaction field (3D-HoVAIF) is used to describe the chemical structures, SMR-PLS QSAR model has been created and good correlation coefficients and cross-validated correlation coefficient is obtained. Predictive capability of the models has also been demonstrated by leave-one-out cross-validation. Moreover, the estimated values have been presented for those PCDD/Fs which are lack of experimentally data by the optimum model.

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