scholarly journals Some topological indices of dendrimers determined by their Banhatti polynomials

2020 ◽  
Vol 26 (1) ◽  
pp. 99-111
Author(s):  
Zheng-Qing Chu ◽  
Muhammad Salman ◽  
Asia Munir ◽  
Imran Khalid ◽  
Masood Ur Rehman ◽  
...  
Keyword(s):  
Molecular Structure ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Graphs

AbstractSeveral properties of chemical compounds in a molecular structure can be determined with the aid of mathematical languages provided by various types of topological indices. In this paper, we consider eight dendrimer structures in the context of valency based topological indices. We define four Banhatti polynomials for general (molecular) graphs, and compute them for underline dendrimers. We use these polynomials to determine four Banhatti indices. We also determine Zagreb (first, second and hyper) and forgotten indices by developing their relationships with Banhatti indices.

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.

scholarly journals On Molecular Topological Properties of TiO2 Nanotubes

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Nilanjan De
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Strong Correlation ◽  
Tio2 Nanotubes ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Properties ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Titania Nanotube

Titania nanotube is a well-known semiconductor and has numerous technological applications. In chemical graph theory, topological indices provide an important tool to quantify the molecular structure and it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Among different topological indices, degree-based topological indices are most studied and have some important applications. In this study, several old and new degree-based topological indices have been investigated for titania TiO2 nanotubes.

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 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 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 Degree-based indices computation for special chemical molecular structures using edge dividing method

2016 ◽  
Vol 1 (1) ◽  
pp. 99-122 ◽  
Author(s):  
Wei Gao ◽  
Mohammad Reza Farahani
Keyword(s):  
Computational Chemistry ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Structures ◽  
Chemical Characteristics ◽  
Molecular Graphs

AbstractIn computational chemistry, the molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bound between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. In this paper, we report several degree based indices of some widely used chemical molecular structures by means of edge dividing technology.

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 M-polynomial-based topological indices of metal-organic networks

2021 ◽  
Vol 44 (1) ◽  
pp. 129-140
Author(s):  
Agha Kashif ◽  
Sumaira Aftab ◽  
Muhammad Javaid ◽  
Hafiz Muhammad Awais
Keyword(s):  
High Surface ◽  
Physical Stability ◽  
High Surface Area ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Energy Storage Devices ◽  
Storage Devices ◽  
Metal Organic ◽  
Relationship Of ◽  
Different Gases

Abstract Topological index (TI) is a numerical invariant that helps to understand the natural relationship of the physicochemical properties of a compound in its primary structure. George Polya introduced the idea of counting polynomials in chemical graph theory and Winer made the use of TI in chemical compounds working on the paraffin's boiling point. The literature of the topological indices and counting polynomials of different graphs has grown extremely since that time. Metal-organic network (MON) is a group of different chemical compounds that consist of metal ions and organic ligands to represent unique morphology, excellent chemical stability, large pore volume, and very high surface area. Working on structures, characteristics, and synthesis of various MONs show the importance of these networks with useful applications, such as sensing of different gases, assessment of chemicals, environmental hazard, heterogeneous catalysis, gas and energy storage devices of excellent material, conducting solids, super-capacitors and catalysis for the purification, and separation of different gases. The above-mentioned properties and physical stability of these MONs become a most discussed topic nowadays. In this paper, we calculate the M-polynomials and various TIs based on these polynomials for two different MONs. A comparison among the aforesaid topological indices is also included to represent the better one.

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