scholarly journals Degree-Based Topological Properties of Molecular Polymeric Networks Composed by Sierpinski Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdul Rauf ◽  
Muhammad Ishtiaq ◽  
Hafiz Faraz Qaiser ◽  
Adnan Aslam ◽  
Kraidi Anoh Yannick
Keyword(s):  
Molecular Graph ◽  
Computer Engineering ◽  
Topological Properties ◽  
Structure Property ◽  
Pharmacological Activities ◽  
Zagreb Index ◽  
Sierpiński Graphs ◽  
Polymeric Networks ◽  
Structure Activity ◽  
Atom Bond

Sierpinski graphs are a widely observed family of fractal-type graphs relevant to topology, Hanoi Tower mathematics, computer engineering, and around. Chemical implementations of graph theory establish significant properties, such as chemical activity, physicochemical properties, thermodynamic properties, and pharmacological activities of a molecular graph. Specific graph descriptors alluded to as topological indices are helpful to predict these properties. These graph descriptors have played a key role in quantitative structure-property/structure-activity relationships (QSPR/QSAR) research. The objective of this article is to compute Randic index ( R − 1 / 2 ), Zagreb index M 1 , sum-connectivity index SCI , geometric-arithmetic index GA , and atom-bond connectivity ABC index based on ev-degree and ve-degree for the Sierpinski networks S n , m .

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 On Topological Indices for New Classes of Benes Network

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Aftab Hussain ◽  
Muhammad Numan ◽  
Nafisa Naz ◽  
Saad Ihsan Butt ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Structure Property ◽  
Structure Activity ◽  
Randić Connectivity Index ◽  
Structure Property Relationship ◽  
Benes Network ◽  
Benes Networks ◽  
Atom Bond

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

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 Bounds on General Randić Index for F-Sum Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xu Li ◽  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Jia-Bao Liu
Keyword(s):  
Molecular Graph ◽  
Randić Index ◽  
Lower And Upper Bounds ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Structure Activity ◽  
General Randić Index ◽  
General Randic Index ◽  
The First Zagreb Index

A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire π-electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the F-sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index RαΓ=∑uv∈EΓdΓu×dΓvα of the F-sum graphs, where α∈R and dΓu denote the valency of the vertex u in the molecular graph Γ. Aim of this paper is to compute the lower and upper bounds of the general Randić index for the F-sum graphs when α∈N. We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly α=1.

Some topological indices of dendrimers

2020 ◽  
pp. 2050018
Author(s):  
S. Alyar ◽  
R. Khoeilar ◽  
A. Jahanbani
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Properties ◽  
Zagreb Index ◽  
Zinc Porphyrin ◽  
Molecular Graphs

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers and analyzed its topological properties. For this purpose, we have computed topological indices, namely the Albertson index, the sigma index, the Nano-Zagreb index, the first and second hyper [Formula: see text]-indices of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers.

scholarly journals Edge Version Molecular Descriptors of Tetrameric 1, 3 Adamantane

2018 ◽  
Vol 7 (4.10) ◽  
pp. 403
Author(s):  
G. Mohanappriya ◽  
D. Vijiyalakshmi
Keyword(s):  
Molecular Descriptors ◽  
Molecular Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Numerical Invariants ◽  
Atom Bond

Molecular descriptors (Topological indices) are the numerical invariants of a molecular graph which distinguish its topology. In this article, we compute edge version of topological indices such as Zagreb index, Atom bond connectivity index, Fourth atom bond connectivity index, Geometric Arithmetic index and Fifth Geometric Arithmetic index of tetrameric 1,3 adamantane. 

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 On Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid‐Anticancer Drug Conjugates with QSPR

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Syed Ajaz K. Kirmani ◽  
Parvez Ali ◽  
Faizul Azam ◽  
Parvez Ahmad Alvi
Keyword(s):  
Molecular Structure ◽  
Hyaluronic Acid ◽  
Biological Activities ◽  
Molecular Graph ◽  
Topological Indices ◽  
Structure Property ◽  
Zagreb Index ◽  
Anticancer Properties ◽  
Drug Conjugates ◽  
Molecular Structure Analysis

The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index ISI α , β ve G and general ve-Zagreb index M α ve G of graph G and compute ISI α , β ve G , M α ve G , and M α ev G (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of ISI α , β ve G , M α ve G , and M α ev G . Furthermore, QSPR analysis of ISI α , β ve G , M α ve G , and M α ev G for particular values of α and β is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.

scholarly journals On Molecular Descriptors of Face-Centered Cubic Lattice

Processes ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 280 ◽  
Author(s):  
Hong Yang ◽  
Muhammad Aamer Rashid ◽  
Sarfraz Ahmad ◽  
Saima Sami Khan ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Cross Section ◽  
Topological Index ◽  
Molecular Descriptors ◽  
Molecular Graph ◽  
Face Centered Cubic ◽  
Topological Properties ◽  
Cubic Lattice ◽  
Face Centered ◽  
Minimal Effort ◽  
Atom Bond

Face-centered cubic lattice F C C ( n ) has received extensive consideration as of late, inferable from its recognized properties and non-poisonous nature, minimal effort, plenitude, and basic creation process. The graph of a face-centered cubic cross-section contains cube points and face centres. A topological index of a molecular graph G is a numeric amount identified with G, which depicts its topological properties. In this paper, using graph theory tools, we computed the molecular descriptors (topological indices)—to be specific, Zagreb-type indices, a forgotten index, a Balaban index, the fourth version of an atom–bond connectivity index, and the fifth version of a geometric arithmetic index for face-centered cubic lattice F C C ( n ) .

scholarly journals Bounds for the Topological Indices of ℘ graph

2021 ◽  
Vol 14 (2) ◽  
pp. 340-350
Author(s):  
Muddalapuram Manjunath ◽  
V. Lokesha ◽  
. Suvarna ◽  
Sushmitha Jain
Keyword(s):  
Finite Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Lower And Upper Bounds ◽  
Zagreb Index ◽  
Chemical Structures ◽  
Structure Property Relationship ◽  
Atom Bond

Topological indices are mathematical measure which correlates to the chemical structures of any simple finite graph. These are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR). In this paper, we define operator graph namely, ℘ graph and structured properties. Also, establish the lower and upper bounds for few topological indices namely, Inverse sum indeg index, Geometric-Arithmetic index, Atom-bond connectivity index, first zagreb index and first reformulated Zagreb index of ℘-graph.

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