scholarly journals On Degree-Based Topological Indices for Strong Double Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Rafiullah ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Kamran Siddiqui ◽  
Mlamuli Dhlamini
Keyword(s):  
Structural Properties ◽  
Topological Index ◽  
Graphical Representation ◽  
Topological Indices ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Characteristic Value ◽  
3D Graphical Representation

A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.

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 On Some Properties of Multiplicative Topological Indices in Silicon-Carbon

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 .

On Certain Topological Indices of Boron Triangular Nanotubes

2017 ◽  
Vol 72 (8) ◽  
pp. 711-716 ◽  
Author(s):  
Adnan Aslam ◽  
Safyan Ahmad ◽  
Wei Gao
Keyword(s):  
Carbon Nanotubes ◽  
Topological Index ◽  
Topological Indices ◽  
Chemical Graph ◽  
Atom Bond

AbstractThe topological index gives information about the whole structure of a chemical graph, especially degree-based topological indices that are very useful. Boron triangular nanotubes are now replacing usual carbon nanotubes due to their excellent properties. We have computed general Randić (Rα), first Zagreb (M1) and second Zagreb (M2), atom-bond connectivity (ABC), and geometric–arithmetic (GA) indices of boron triangular nanotubes. Also, we have computed the fourth version of atom-bond connectivity (ABC4) and the fifth version of geometric–arithmetic (GA5) indices of boron triangular nanotubes.

scholarly journals Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zhen Wang ◽  
Faryal Chaudhry ◽  
Maria Naseem ◽  
Adnan Asghar
Keyword(s):  
Molecular Descriptor ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Crystallographic Structure ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory ◽  
Structure Of Molecules ◽  
Wet Lab ◽  
Ga Index

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. Topological indices help us collect information about algebraic graphs and give us mathematical approach to understand the properties of algebraic structures. With the help of topological indices, we can guess the properties of chemical compounds without performing experiments in wet lab. There are more than 148 topological indices in the literature, but none of them completely give all properties of under study compounds. Together, they do it to some extent; hence, there is always room to introduce new indices. In this paper, we present first and second reserve Zagreb indices and first reverse hyper-Zagreb indices, reverse GA index, and reverse atomic bond connectivity index for the crystallographic structure of molecules. We also present first and second reverse Zagreb polynomials and first and second reverse hyper-Zagreb polynomials for the crystallographic structure of molecules.

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.

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 M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muhammad Irfan ◽  
Hamood Ur Rehman ◽  
Hassan Almusawa ◽  
Saffina Rasheed ◽  
Imran Abbas Baloch
Keyword(s):  
Graph Theory ◽  
Topological Index ◽  
Chemical Properties ◽  
Topological Indices ◽  
Line Graphs ◽  
Silicate Network ◽  
Chemical Graph ◽  
Chain Silicate

Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

scholarly journals Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Hai-Xia Li ◽  
Sarfaraz Ahmad ◽  
Iftikhar Ahmad
Keyword(s):  
Topological Index ◽  
Molecular Descriptor ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Chemical Graph Theory ◽  
Augmented Zagreb Index

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In this paper, M-polynomial OKn and OPn networks are computed. The M-polynomial is rich in information about degree-based topological indices. By applying the basic rules of calculus on M-polynomials, the first and second Zagreb indices, modified second Zagreb index, general Randić index, inverse Randić index, symmetric division index, harmonic index, inverse sum index, and augmented Zagreb index are recovered.

scholarly journals Computing SS Index of Certain Dendrimers

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.

scholarly journals Molecular Properties of Symmetrical Networks Using Topological Polynomials

2019 ◽  
Vol 17 (1) ◽  
pp. 849-864 ◽  
Author(s):  
Xing-Long Wang ◽  
Jia-Bao Liu ◽  
Maqsood Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Hussain ◽  
...  
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Chemical Species ◽  
Chemical Properties ◽  
Biological Properties ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Physico Chemical ◽  
Symmetry Properties ◽  
Physical Features

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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