scholarly journals Modified Zagreb connection indices of the T-sum graphs

2020 ◽  
Vol 43 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Usman Ali ◽  
Muhammad Javaid ◽  
Agha Kashif
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Line Graphs ◽  
Real Numbers ◽  
Statistical Tools ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Octane Isomers

AbstractThe quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

scholarly journals Zagreb Connection Indices of Two Dendrimer Nanostars

2019 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Nisar Fatima ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Physicochemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Octane Isomers ◽  
The First Zagreb Index

Abstract It is well known fact that several physicochemical properties of chemical compounds are closely related to their molecular structure. Mathematical chemistry provides a method to predict the aforementioned properties of compounds using topological indices. The Zagreb indices are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [Ali, A.; Trinajstić, N. A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO] 2017; Mol. Inform. 2018, 37, 1800008] and [Naji, A. M.; Soner, N. D.; Gutman, I. On leap Zagreb indices of graphs, Commun. Comb. Optim. 2017, 2, 99–117], which were named as the Zagreb connection indices and the leap Zagreb indices, respectively. In this paper, we check the chemical applicability of the newly considered Zagreb connection indices on the set of octane isomers and establish general expressions for calculating these indices of two well-known dendrimer nanostars.

scholarly journals Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices of Generalized Bridge Molecular Graphs

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 751 ◽  
Author(s):  
Xiujun Zhang ◽  
Xinling Wu ◽  
Shehnaz Akhter ◽  
Muhammad Jamil ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Industry Research ◽  
Chemical Graph Theory ◽  
Chain Polymerization ◽  
Definition Of ◽  
Atom Bond

Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we propose a definition of generalized bridge molecular graphs that can model more kinds of long chain polymerization products than the bridge molecular graphs, and provide some results of the edge versions of atom-bond connectivity ( A B C e ) and geometric arithmetic ( G A e ) indices for some generalized bridge molecular graphs, which have regular, periodic and symmetrical structures. The results of this paper offer promising prospects in the applications for chemical and material engineering, especially in chemical industry research.

scholarly journals General Fifth M- Zagreb Polynomials of the TUC4C8(R)[p, q] 2D-Lattice and its Derived Graphs

2020 ◽  
Vol 10 (1) ◽  
pp. 1738-1747
Keyword(s):  
Chemical Compound ◽  
Molecular Graph ◽  
Vital Role ◽  
Topological Indices ◽  
Line Graphs ◽  
Topological Properties ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Physical Chemical

A molecular graph or a chemical graph is a graph related to the structure of a chemical compound. The topological indices play a vital role in understanding the physical, chemical, and topological properties of the respective compound. ln this article, we discuss the computation of the degree-based topological indices, namely - the fifth M-Zagreb indices and their polynomials, fifth hyper M-Zagreb indices and their polynomials, general fifth M-Zagreb indices and their polynomials, third Zagreb index and it is polynomial for the TUC_4 C_8 (R)[p,q] lattice, its subdivision, and para-line graphs.

scholarly journals Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Jia Bao Liu ◽  
Sana Akram ◽  
Muhammad Javaid ◽  
Abdul Raheem ◽  
Roslan Hasni
Keyword(s):  
Structural Properties ◽  
Electron Energy ◽  
Boiling Point ◽  
Molecular Descriptors ◽  
Molecular Descriptor ◽  
Molecular Graph ◽  
Topological Indices ◽  
Real Numbers ◽  
Molecular Graphs

A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π -electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randić are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the bounds of the aforesaid TIs for the generalized F -sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized F -sum graphs as the consequences of the obtained results. At the end, 3   D -graphical presentations are also included to illustrate the results for better understanding.

scholarly journals Computing entire Zagreb indices of some dendrimer structures

2020 ◽  
Vol 43 (1) ◽  
pp. 229-236
Author(s):  
Wei Gao ◽  
Zahid Iqbal ◽  
Abdul Jaleel ◽  
Adnan Aslam ◽  
Muhammad Ishaq ◽  
...  
Keyword(s):  
Molecular Level ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Chemical Methods ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Qspr Study

AbstractTopological indices are numerical numbers associated to molecular graphs and are invariant of a graph. In QSAR/QSPR study, Zagreb indices are used to explain the different properties of chemical compounds at the molecular level mathematically. They have been studied extensively due to their ease of calculation and numerous applications in place of the existing chemical methods which needed more time and increased the costs. In this paper, we compute precise values of new versions of Zagreb indices for two classes of dendrimers.

scholarly journals Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

2019 ◽  
Vol 17 (1) ◽  
pp. 260-266 ◽  
Author(s):  
Imran Nadeem ◽  
Hani Shaker ◽  
Muhammad Hussain ◽  
Asim Naseem
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Structural Chemistry ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

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 Computation of Zagreb and atom-bond connectivity indices of certain families of dendrimers by using automorphism group action

2017 ◽  
Vol 82 (2) ◽  
pp. 151-162
Author(s):  
Uzma Ahmad ◽  
Sarfraz Ahmad ◽  
Rabia Yousaf
Keyword(s):  
Automorphism Group ◽  
Carbon Atom ◽  
Physicochemical Properties ◽  
Group Action ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Connectivity Indices ◽  
Atom Bond

In QSAR/QSPR studies, topological indices are utilized to predict the bioactivity of chemical compounds. In this paper, the closed forms of different Zagreb indices and atom?bond connectivity indices of regular dendrimers G[n] and H[n] in terms of a given parameter n are determined by using the automorphism group action. It was reported that these connectivity indices are correlated with some physicochemical properties and are used to measure the level of branching of the molecular carbon-atom skeleton.

scholarly journals Valency-based molecular descriptors of Bakelite network BNmn$B\text N_{m}^{n}$

2019 ◽  
Vol 17 (1) ◽  
pp. 663-670 ◽  
Author(s):  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Chahn Yong Jung
Keyword(s):  
Physical Properties ◽  
Molecular Descriptors ◽  
Molecular Graph ◽  
Synthetic Polymer ◽  
Topological Indices ◽  
Qsar Studies ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Atom Bond

AbstractBakelite network $BN_{m}^{n}$is a molecular graph of bakelite, a pioneering and revolutionary synthetic polymer (Thermosetting Plastic) and regarded as the material of a thousand uses. In this paper, we aim to compute various degree-based topological indices of a molecular graph of bakelite network $BN_{m}^{n}$. These molecular descriptors play a fundamental role in QSPR/QSAR studies in describing the chemical and physical properties of Bakelite network $BN_{m}^{n}$. We computed atom-bond connectivity ABC its fourth version ABC4 geometric arithmetic GA its fifth version GA5 Narumi-Katayama, sum-connectivity and Sanskruti indices, first, second, modified and augmented Zagreb indices, inverse and general Randic’ indices, symmetric division, harmonic and inverse sum indices of $BN_{m}^{n}$.

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.

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