scholarly journals On Computation of Edge Degree-Based Banhatti Indices of a Certain Molecular Network

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiang-Hua Tang ◽  
Muhammad Abid ◽  
Kashif Ali ◽  
Asfand Fahad ◽  
Muhammad Anwar Chaudhry ◽  
...  
Keyword(s):  
Drug Delivery ◽  
Graph Theory ◽  
Molecular Descriptors ◽  
Molecular Graph ◽  
Molecular Structures ◽  
Water Soluble ◽  
Molecular Network ◽  
Chemical Graph ◽  
Basic Properties ◽  
Chemical Graph Theory

Chemical graph theory deals with the basic properties of a molecular graph. In graph theory, we correlate molecular descriptors to the properties of molecular structures. Here, we compute some Banhatti molecular descriptors for water-soluble dendritic unimolecular polyether micelle. Our results prove to be very significant to understand the behaviour of water-soluble dendritic unimolecular polyether micelle as a drug-delivery agent.

scholarly journals Topological Indices of Carbon Graphite and Crystal Cubic Carbon Structures via M Polynomials

2018 ◽  
Author(s):  
Wei Gao ◽  
Waqas Nazeer ◽  
Amna Yousaf ◽  
Shin Min Kang
Keyword(s):  
Graph Theory ◽  
Chemical Structure ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Chemical Graph ◽  
Boiling Points ◽  
Chemical Graph Theory ◽  
Carbon Structures ◽  
Carbon Crystal

Graph theory plays a crucial role in modeling and designing of chemical structure or chemical network. Chemical Graph theory helps to understand the molecular structure of molecular graph. The molecular graph consists of atoms as vertices and bonds as edges. Topological indices capture symmetry of molecular structures and give it a mathematical language to predict properties such as boiling points, viscosity, the radius of gyrations etc. In this article, we study the chemical graph of carbon Crystal structure of graphite and cubic carbon and compute several degree-based topological indices. Firstly we compute M-Polynomials of these structures and then from these M-polynomials we recover nine degree-based topological indices.

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
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.

Graph Applications in Chemoinformatics and Structural Bioinformatics

2011 ◽  
pp. 386-420
Author(s):  
Eleanor Joyce Gardiner
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Structural Bioinformatics ◽  
Three Dimensions ◽  
Chemical Graph ◽  
Labeled Graph ◽  
3D Space ◽  
Chemical Graph Theory ◽  
Computer Representation ◽  
History Of

The focus of this chapter will be the uses of graph theory in chemoinformatics and in structural bioinformatics. There is a long history of chemical graph theory dating back to the 1860’s and Kekule’s structural theory. It is natural to regard the atoms of a molecule as nodes and the bonds as edges (2D representations) of a labeled graph (a molecular graph). This chapter will concentrate on the algorithms developed to exploit the computer representation of such graphs and their extensions in both two and three dimensions (where an edge represents the distance in 3D space between a pair of atoms), together with the algorithms developed to exploit them. The algorithms will generally be summarized rather than detailed. The methods were later extended to larger macromolecules (such as proteins); these will be covered in less detail.

scholarly journals On Computation Degree-Based Topological Descriptors for Planar Octahedron Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wang Zhen ◽  
Parvez Ali ◽  
Haidar Ali ◽  
Ghulam Dustigeer ◽  
Jia-Bao Liu
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Descriptors ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Symmetric Division ◽  
Chemical Graph Theory ◽  
Augmented Zagreb Index

A molecular graph is used to represent a chemical molecule in chemical graph theory, which is a branch of graph theory. A graph is considered to be linked if there is at least one link between its vertices. A topological index is a number that describes a graph’s topology. Cheminformatics is a relatively young discipline that brings together the field of sciences. Cheminformatics helps in establishing QSAR and QSPR models to find the characteristics of the chemical compound. We compute the first and second modified K-Banhatti indices, harmonic K-Banhatti index, symmetric division index, augmented Zagreb index, and inverse sum index and also provide the numerical results.

scholarly journals Molecular description of copper(II) oxide

2017 ◽  
Vol 36 (1) ◽  
Author(s):  
Mohammad Reza Farahani ◽  
Wei Gao ◽  
Abdul Qudair Baig ◽  
Wasaq Khalid
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Theoretical Chemistry ◽  
Topological Descriptors ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Mathematical Chemistry ◽  
Chemical Graph Theory ◽  
Numerical Invariants ◽  
Molecular Description

Graph theory has much advancement in the field of mathematical chemistry. Recently, chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields.In this article, we study the chemical graph of copper oxide and compute degree based topological indices mainly ABC, GA, ABC4, GA5, general Randić index and Zagreb index for copper(II) oxide, CuO. Furthermore, we give exact formulas of these indices which are helpful in studying the underlying topologies.

Graph Applications in Chemoinformatics and Structural Bioinformatics

2013 ◽  
pp. 1126-1157 ◽  
Author(s):  
Eleanor Joyce Gardiner
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Structural Bioinformatics ◽  
Three Dimensions ◽  
Chemical Graph ◽  
Labeled Graph ◽  
3D Space ◽  
Chemical Graph Theory ◽  
Computer Representation ◽  
History Of

The focus of this chapter will be the uses of graph theory in chemoinformatics and in structural bioinformatics. There is a long history of chemical graph theory dating back to the 1860’s and Kekule’s structural theory. It is natural to regard the atoms of a molecule as nodes and the bonds as edges (2D representations) of a labeled graph (a molecular graph). This chapter will concentrate on the algorithms developed to exploit the computer representation of such graphs and their extensions in both two and three dimensions (where an edge represents the distance in 3D space between a pair of atoms), together with the algorithms developed to exploit them. The algorithms will generally be summarized rather than detailed. The methods were later extended to larger macromolecules (such as proteins); these will be covered in less detail.

scholarly journals Banhatti, revan and hyper-indices of silicon carbide Si2C3-III[n,m]

2021 ◽  
Vol 19 (1) ◽  
pp. 646-652
Author(s):  
Dongming Zhao ◽  
Manzoor Ahmad Zahid ◽  
Rida Irfan ◽  
Misbah Arshad ◽  
Asfand Fahad ◽  
...  
Keyword(s):  
Silicon Carbide ◽  
Graph Theory ◽  
Topological Index ◽  
Molecular Graph ◽  
Graphical Analysis ◽  
Topological Indices ◽  
Chemical Bonds ◽  
Chemical Graph ◽  
Molecular Graphs ◽  
Chemical Graph Theory

Abstract In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph G G of a molecule consists of vertices and edges, where vertices represent the atoms in a molecule and edges represent the chemical bonds between these atoms. A numerical quantity that gives information related to the topology of the molecular graphs is called a topological index. Several topological indices, contributing to chemical graph theory, have been defined and vastly studied. Recent inclusions in the class of the topological indices are the K-Banhatti indices. In this paper, we established the precise formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] . In addition, we present the graphical analysis along with the comparison of these indices for Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] .

Computing the Theta Polynomial Θ(G, x) and the Theta Index Θ(G) of Titania Nanotubes TiO2(m, n)

2017 ◽  
Vol 14 (1) ◽  
pp. 715-717
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Mohammad R Farahani ◽  
Muhammad Imran ◽  
Muhammad K Jamil
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Infinite Family ◽  
Titania Nanotubes ◽  
Chemical Graph ◽  
First Derivative ◽  
Chemical Graph Theory ◽  
Omega Polynomial ◽  
Definition Of ◽  
First Time

Let G = (V,E) be a simple connected molecular graph in chemical graph theory, where the vertex/atom set and edge/bond set of G denoted by V(G) and E(G), respectively and its vertices correspond to the atoms and the edges correspond to the bonds. Two counting polynomials the “Omega Ω(G,x) and Theta Θ(G,x)” polynomials of a molecular graph G were defined by Diudea as Ω(G,x) = ΣeE(G) xn(E) and Θ(G,x) = ΣeE(G) xn(E), where n(E) denotes the number of edges co-distant with the edge E. From definition of these counting polynomials, we can obtain the Theta polynomial by inserting the coefficient n(E) in the Omega polynomial. Then the Theta index will be the first derivative of the Theta polynomial Θ(G,x) evaluated at x = 1. The goal of this paper is to compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of an infinite family of the Titania Nanotubes TiO2(m,n) for the first time.

scholarly journals Topological Descriptor of 2-Dimensional Silicon Carbons and Their Applications

2019 ◽  
Vol 17 (1) ◽  
pp. 1473-1482 ◽  
Author(s):  
Muhammad Nadeem ◽  
Sarfraz Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Naeem
Keyword(s):  
Graph Theory ◽  
Molecular Structures ◽  
Chemical Bonds ◽  
Chemical Graph ◽  
Topological Descriptor ◽  
Chemical Graph Theory ◽  
Silicon Carbon

AbstractThe Chemical graph theory is extensively used in finding the atomic supplementary properties of different chemical stuructures. Many results of graph theory are commonly used in molecular structures and in general in Chemisty. In a molcular graph vertices are atoms while chemical bonds are given by edges. This article is about computing the exact values for some degree based toplogical descriptors of two molecular structures. Namely we work on the silicon-carbon Si2C3- III and SiC3-III for dimension two. We also discuss some applications of these results towards Chemistry.

scholarly journals Eccentricity Based Topological Indices of an Oxide Network

Mathematics ◽  
2018 ◽  
Vol 6 (7) ◽  
pp. 126 ◽  
Author(s):  
Muhammad Imran ◽  
Muhammad Siddiqui ◽  
Amna Abunamous ◽  
Dana Adi ◽  
Saida Rafique ◽  
...  
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Theoretical Chemistry ◽  
Topological Descriptors ◽  
Chemical Graph ◽  
Mathematical Chemistry ◽  
Chemical Graph Theory ◽  
Numerical Invariants ◽  
Average Eccentricity ◽  
Atom Bond

Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields. In this article, we study the chemical graph of an oxide network and compute the total eccentricity, average eccentricity, eccentricity based Zagreb indices, atom-bond connectivity (ABC) index and geometric arithmetic index of an oxide network. Furthermore, we give analytically closed formulas of these indices which are helpful in studying the underlying topologies.

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