scholarly journals The Calculations of Topological Indices on Certain Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jia-Bao Liu ◽  
Ting Zhang ◽  
Sakander Hayat
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Chemical Graph ◽  
The Core ◽  
Chemical Graph Theory ◽  
Definition Of ◽  
Internal Relationship

It is one of the core problems in the study of chemical graph theory to study the topological index of molecular graph and the internal relationship between its structural properties and some invariants. In recent years, topological index has been gradually applied to the models of QSAR and QSPR . In this work, using the definition of the ABC index, AZI index, GA index, the multiplicative version of ordinary first Zagreb index, the second multiplicative Zagreb index, and Zagreb index, we calculate the degree-based topological indices of some networks. Then, the above indices’ formulas are obtained.

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 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] .

scholarly journals Topological Indices of H-Naphtalenic Nanosheet

2018 ◽  
Vol 16 (1) ◽  
pp. 1184-1188 ◽  
Author(s):  
Nazeran Idrees ◽  
Muhammad Jawwad Saif ◽  
Afshan Sadiq ◽  
Asia Rauf ◽  
Fida Hussain
Keyword(s):  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Second Zagreb Index ◽  
Topological Descriptor ◽  
Chemical Graph Theory ◽  
Atom Bond

AbstractIn chemical graph theory, a single numeric number related to a chemical structure is called a topological descriptor or topological index of a graph. In this paper, we compute analytically certain topological indices for H-Naphtalenic nanosheet like Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper-Zagreb index using edge partition technique. The first multiple Zagreb index and the second multiple Zagreb index of the nanosheet are also discussed in this paper.

scholarly journals The Generalized Zagreb Index of Some Carbon Structures

2018 ◽  
Vol 26 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Prosanta Sarkar ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Topological Indices ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Carbon Structures

Abstract In chemical graph theory, chemical structures are model edthrough a graph where atoms are considered as vertices and edges are bonds between them. In chemical sciences, topological indices are used for understanding the physicochemical properties of molecules. In this work, we study the generalized Zagreb index for three types of carbon allotrope’s theoretically.

Physical Analysis of Heat of Formation and Entropy for Ceria Oxide Using Topological Indices

2020 ◽  
Vol 23 ◽  
Author(s):  
Xiujun Zhang ◽  
Muhammad Kamran Siddiqui ◽  
Sana Javed ◽  
Lubna Sherin ◽  
Farah Kausar ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Heat Of Formation ◽  
Topological Indices ◽  
Physical Analysis ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Vertex Partition ◽  
Numerical Invariants ◽  
Ceria Oxide ◽  
Matlab Programming

Background:: “Cerium oxide nanoparticles ( Aim and Objective:: The study“was aimed to analyze the chemical graph of crystal structure of Ceria Oxide(cuprite) Materials and Methods:: Chemical“graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. For calculation, we have utilized the combinatorial processing strategy, edge partition technique, vertex partition strategy, analytic procedures, graph hypothetical tools, degree counting technique and entirety of degrees of neighbors technique. Moreover, Matlab programming have been utilized for the numerical computations and checks. We likewise utilized the maple for plotting these numerical outcomes.” Results:: We have“computed Heat of Formation and Entropy using degree based topological indices. More oreciously, our main results are based on some degree based topological indices, namely, the atom bond connectivity index Conclusion:: We discuss“these indices exhibited difference with the reported heat of formation and entropy of cuprite

scholarly journals On Realization and Characterization of Topological Indices

2019 ◽  
Vol 9 (1) ◽  
pp. 715-718
Keyword(s):  
Topological Index ◽  
Fixed Number ◽  
Topological Indices ◽  
Molecular Structures ◽  
Real Numbers ◽  
Graph Invariants ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory

In chemical graph theory, topological index is one of the graph invariants which is a fixed number based on structure of a graph. Topological index is used as one of the tool to analyze molecular structures and for proper and optimal design of nanostructure. In this paper we realize the real numbers that are topological indices such as Zagreb indices, Randic index, NK-index, multiplicative F-index and multiplicative Zagreb indices along with some characterizations.

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 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.

scholarly journals Topological Indices of Some New Graph Operations and Their Possible Applications

2021 ◽  
pp. 16-30
Author(s):  
Abdu Qaid Saif Alameri ◽  
Mohammed Saad Yahya Al-Sharafi
Keyword(s):  
Graph Theory ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Structural Invariant ◽  
Graph Operations ◽  
Chemical Graph Theory ◽  
Cyclic Alkanes ◽  
The First Zagreb Index

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

On topological indices of a carbon nanotube network

2015 ◽  
Vol 93 (10) ◽  
pp. 1157-1160 ◽  
Author(s):  
Martin Bača ◽  
Jarmila Horváthová ◽  
Martina Mokrišová ◽  
Andrea Semaničová-Feňovčíková ◽  
Alžbeta Suhányiová
Keyword(s):  
Carbon Nanotube ◽  
Topological Index ◽  
Hexagonal Lattice ◽  
Topological Indices ◽  
Important Class ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Carbon Nanotube Network ◽  
Vertex Degrees ◽  
Atom Bond

A numerical quantity that characterizes the whole structure of a graph is called a topological index. The concept of Randić (Rα), atom−bond connectivity (ABC), and geometric−arithmetic (GA) topological indices was established in chemical graph theory based on vertex degrees. In this paper, we study a carbon nanotube network that is motivated by the molecular structure of a regular hexagonal lattice and determine Rα, ABC, and GA indices for this important class of networks.

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