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 .

scholarly journals On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 320 ◽  
Author(s):  
Young Kwun ◽  
Abaid Virk ◽  
Waqas Nazeer ◽  
M. Rehman ◽  
Shin Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Compound ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Physico Chemical ◽  
Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

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 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 Zagreb Polynomials and Redefined Zagreb Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

2018 ◽  
Author(s):  
Young Chel Kwun ◽  
Abaid ur Rehman Virk ◽  
Waqas Nazeer ◽  
Wei Gao ◽  
Shin Min Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Structure Research

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q]. We compute several Zagreb polynomials and Redefined Zagreb indices of these silicon-carbons.

scholarly journals Computing FGZ Index of Sum Graphs under Strong Product

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhi-Ba Peng ◽  
Saira Javed ◽  
Muhammad Javaid ◽  
Jia-Bao Liu
Keyword(s):  
Structural Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Zagreb Index ◽  
Strong Product ◽  
Product Of Graphs

Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related operations and strong product of graphs which create hexagonal chains isomorphic to many chemical compounds. Mainly, the exact values of first general Zagreb index (FGZI) for four sum graphs are obtained. At the end, FGZI of the two particular families of sum graphs are also computed as applications of the main results. Moreover, the dominating role of the FGZI among these sum graphs is also shown using the numerical values and their graphical presentations.

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 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.

scholarly journals Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aqsa Sattar ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Chemical Structures ◽  
And Mathematics

The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

scholarly journals On Sombor Index

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 140
Author(s):  
Kinkar Chandra Das ◽  
Ahmet Sinan Çevik ◽  
Ismail Naci Cangul ◽  
Yilun Shang
Keyword(s):  
Graph Theory ◽  
Topological Index ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory ◽  
Degree Of Vertex ◽  
Graph Parameters ◽  
Future Work

The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

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.

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