scholarly journals On Topological Indices of Dual Graph of Benzene Ring Embedded in P-Type Surface in 2D Network

2021 ◽  
Vol 10 (3) ◽  
pp. 1936-1941
Keyword(s):  
Benzene Ring ◽  
Molecular Graph ◽  
Dual Graph ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Abc Index ◽  
P Type ◽  
2D Network ◽  
Ga Index ◽  
Atom Bond

The structure of any finite molecular graph which represent numerical quantities are known as topological indices. The importance of topological indices is generally linked with QSAR/QSPR. In this paper, we compute general Zagreb (M஑_) index, general Randic connectivity (R஑_) index, general sum-connectivity (χ஑) index, atom-bond connectivity (ABC) index, and geometric-arithmetic (GA) index,ABCସ, GAହ, multiple Zagreb indices and Zagreb polynomial indices of the of dual graph of benzene ring embedded in P-type-surface in 2D network.

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 General Fifth M-Zagreb Polynomials of Benzene Ring Implanted in the P-Type-Surface in 2D Network

2020 ◽  
Vol 10 (6) ◽  
pp. 6881-6892 ◽  
Keyword(s):  
Molecular Structure ◽  
Benzene Ring ◽  
Biological Properties ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Activity ◽  
Physical Chemical ◽  
P Type ◽  
2D Network

Constitutional formulae of molecules are molecular graphs consisting of atoms as vertices and bonds between them represented as edges. The various physical, chemical, and biological properties of molecules are dependent on their molecular structures. The molecular structure is most important, not only to chemists but also to all scientists. The molecular structure descriptors or topological indices of molecules are a mathematical number or a set of selected invariants of matrices that are used to Quantitative Structure-Activity (-Property) Relationships (QSAR/QSPR) studies. In this paper, we computed some new degree-based topological indices of benzene ring implanted in the P-type-surface in the 2D network and its line subdivision of graph.

scholarly journals On Degree-Based Topological Indices of Symmetric Chemical Structures

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 619 ◽  
Author(s):  
Jia-Bao Liu ◽  
Haidar Ali ◽  
Muhammad Shafiq ◽  
Usman Munir
Keyword(s):  
Molecular Descriptor ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Chemical Structures ◽  
Physico Chemical ◽  
First Time ◽  
Ga Index ◽  
Atom Bond

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randić index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

scholarly journals Computing multiple ABC index and multiple GA index of some grid graphs

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 588-598 ◽  
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Naeem ◽  
Muhammad Imran
Keyword(s):  
Boiling Point ◽  
Chemical Compounds ◽  
Enthalpy Of Vaporization ◽  
Topological Indices ◽  
Grid Graphs ◽  
Square Grid ◽  
Abc Index ◽  
Atomic Descriptors ◽  
Ga Index ◽  
Atom Bond

AbstractTopological indices are the atomic descriptors that portray the structures of chemical compounds and they help us to anticipate certain physico-compound properties like boiling point, enthalpy of vaporization and steadiness. The atom bond connectivity (ABC) index and geometric arithmetic (GA) index are topological indices which are defined as $ABC(G)=\sum_{uv\in E(G)}\sqrt{\frac{d_u+d_v-2}{d_ud_v}}$ and $GA(G)=\sum_{uv\in E(G)}\frac{2\sqrt{d_ud_v}}{d_u+d_v}$ , respectively, where du is the degree of the vertex u. The aim of this paper is to introduced the new versions of ABC index and GA index namely multiple atom bond connectivity (ABC) index and multiple geometric arithmetic (GA) index. As an application, we have computed these newly defined indices for the octagonal grid $O_p^q$ , the hexagonal grid H(p, q) and the square grid Gp, q. Also, we compared these results obtained with the ones by other indices like the ABC4 index and the GA5 index.

On the Certain Topological Indices of Titania Nanotube TiO2[m, n]

2017 ◽  
Vol 72 (7) ◽  
pp. 647-654 ◽  
Author(s):  
M. Javaid ◽  
Jia-Bao Liu ◽  
M. A. Rehman ◽  
Shaohui Wang
Keyword(s):  
Chemical Compound ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Mathematical Expressions ◽  
Titania Nanotube ◽  
Physical Features ◽  
Atom Bond

AbstractA numeric quantity that characterises the whole structure of a molecular graph is called the topological index that predicts the physical features, chemical reactivities, and boiling activities of the involved chemical compound in the molecular graph. In this article, we give new mathematical expressions for the multiple Zagreb indices, the generalised Zagreb index, the fourth version of atom-bond connectivity (ABC4) index, and the fifth version of geometric-arithmetic (GA5) index of TiO2[m, n]. In addition, we compute the latest developed topological index called by Sanskruti index. At the end, a comparison is also included to estimate the efficiency of the computed indices. Our results extended some known conclusions.

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 M-Polynomial and Topological Indices of Benzene Ring Embedded in P-Type Surface Network

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Hong Yang ◽  
A. Q. Baig ◽  
W. Khalid ◽  
Mohammad Reza Farahani ◽  
Xiujun Zhang
Keyword(s):  
Benzene Ring ◽  
Graphical Representation ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Surface Network ◽  
P Type

The representation of chemical compounds and chemical networks with the M-polynomials is a new idea, and it gives nice and good results of the topological indices. These results are used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. In this article, particular attention will be put on the derivation of M-polynomial for the benzene ring embedded in the P-type surface network in 2D. Furthermore, the topological indices based on the degrees are also derived by using the general form of M-polynomial of the benzene ring embedded in the P-type surface network BRm,n. In the end, the graphical representation and comparison of the M-polynomial and the topological indices of the benzene ring embedded in the P-type surface network in 2D are described.

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