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 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.

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 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 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 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 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 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 $BN_{m}^{n}$.

On degree-based topological descriptors of strong product graphs

2016 ◽  
Vol 94 (6) ◽  
pp. 559-565 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Zagreb Indices ◽  
Strong Product ◽  
Product Graphs ◽  
Product Of Graphs ◽  
Atom Bond

Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

On topological indices of poly oxide, poly silicate, DOX, and DSL networks

2015 ◽  
Vol 93 (7) ◽  
pp. 730-739 ◽  
Author(s):  
Abdul Qudair Baig ◽  
Muhammad Imran ◽  
Haidar Ali
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Physicochemical Properties ◽  
Interconnection Networks ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Silicate Network ◽  
Graph Invariant ◽  
Qspr Study ◽  
Atom Bond

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices 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 different interconnection networks and derive analytical closed results of the general Randić index (Rα(G)) for α = 1, [Formula: see text], –1, [Formula: see text] only, for dominating oxide network (DOX), dominating silicate network (DSL), and regular triangulene oxide network (RTOX). All of the studied interconnection networks in this paper are motivated by the molecular structure of a chemical compound, SiO4. We also compute the general first Zagreb, ABC, GA, ABC4, and GA5 indices and give closed formulae of these indices for these interconnection networks.

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