scholarly journals Computation of Polynomial Degree-Based Topological Descriptors of Indu-Bala Product of Two Paths

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Ghazanfar Abbas ◽  
Muhammad Ibrahim
Keyword(s):  
Graphical Representation ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Basic Sciences ◽  
Polynomial Degree ◽  
Degree Of Vertex ◽  
Reasonable Proportion ◽  
Network Properties

Cheminformatics is entirely a newly coined term that encompasses a field that includes engineering computer sciences along with basic sciences. As we all know, vertices and edges form a network whereas vertex and its degrees contribute to joining edges. The degree of vertex is very much dependent on a reasonable proportion of network properties. There is no doubt that a network has to have a reliance of different kinds of hub buses, serials, and other connecting points to constitute a system that is the backbone of cheminformatics. The Indu-Bala product of two graphs G 1 and G 2 has a special notation as described in Section 2. The attainment of this product is very much due to related vertices at to different places of G 1 ∨ G 2 . This study states we have found M-polynomial and degree-based topological indices for Indu-Bala product of two paths P k and P j for j , k ≥ 2 . We also give some graphical representation of these indices and analyzed them graphically.

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Water Soluble ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Physical And Chemical Properties ◽  
Eccentric Connectivity Index ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

ON VE-DEGREE AND EV-DEGREE BASED TOPOLOGICAL INDICES OF CERTAIN OTIS BISWAPPED NETWORK

2021 ◽  
Vol 10 (6) ◽  
pp. 2887-2908
Author(s):  
N. Zahra ◽  
M. Ibrahim
Keyword(s):  
Present Article ◽  
Complete Graph ◽  
Interconnection Networks ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Numerous Application

The optical transpose interconnection system (OTIS) arrange has numerous application in designed for equal just as in conveyed arrange. Distinctive interconnection networks has contemplated identified with topological descriptors in [\cite{25,26}]. The present article is a contribution to Ve-degree and Ev-degree base topological indices of biswapped network with premise diagram as path and complete graph. In addition, some delicated recipes are too gotten for various kinds of topological records for the OTIS biswapped network by taking the path and complete graph on $n$ vertices as premise of diagram.

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.

scholarly journals M-Polynomial and Degree Based Topological Indices of Some Nanostructures

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 831 ◽  
Author(s):  
Zahid Raza ◽  
Mark Essa K. Sukaiti
Keyword(s):  
Graphical Representation ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Detailed Comparison ◽  
Topological Indices ◽  
Chemical Structures

The association of M-polynomial to chemical compounds and chemical networks is a relatively new idea, and it gives good results about the topological indices. These results are then used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. In this paper, an effort is made to compute the general form of the M-polynomials for two classes of dendrimer nanostars and four types of nanotubes. These nanotubes have very nice symmetries in their structural representations, which have been used to determine the corresponding M-polynomials. Furthermore, by using the general form of M-polynomial of these nanostructures, some degree-based topological indices have been computed. In the end, the graphical representation of the M-polynomials is shown, and a detailed comparison between the obtained topological indices for aforementioned chemical structures is discussed.

On Topological Properties of 2-Dimensional Lattices of Carbon Nanotubes

2016 ◽  
Vol 13 (10) ◽  
pp. 6606-6615
Author(s):  
Sakander Hayat ◽  
Muhammad Kashif Shafiq ◽  
Asad Khan ◽  
Hassan Raza ◽  
Hafiz Muhmmad Afzal Siddiqui ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Quaternary Structure ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Structure Property ◽  
Specific Chemical ◽  
Carbon Nanosheets ◽  
Chemical Significance ◽  
Numerical Invariants ◽  
Intermediate Size

Topological descriptors are the most important numerical quantities in the fields of mathematical chemistry and nanotechnology. These numerical descriptors are based on the topology of the atoms and their bonds (chemical conformation, quaternary structure). Local-valency/degree based topological descriptors/indices are of vital importance due to their specific chemical significance. These numerical invariants are the most successful molecular descriptors in structure-property and structure-activity relationships studies. A nanostructure is an object of intermediate size between molecular and microscopic structures. It is a product derived through engineering at the molecular scale. The most important of these new materials are carbon nanotubes. They have remarkable electronic properties and many other unique characteristics. Carbon nanosheets are 2-dimensional lattices of carbon nanotubes. To compute and study topological indices of nanostructures is a respected problem in nanotechnology. In this paper, degree based topological indices of certain carbon nanosheets are strong-minded. We formulate an important conjecture at the end of this article.

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.

scholarly journals Valency-Based Topological Properties of Linear Hexagonal Chain and Hammer-Like Benzenoid

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yi-Xia Li ◽  
Abdul Rauf ◽  
Muhammad Naeem ◽  
Muhammad Ahsan Binyamin ◽  
Adnan Aslam
Keyword(s):  
Graphical Representation ◽  
Structural Features ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Hexagonal Chain ◽  
Structure Property Relationships ◽  
Quantitative Measurements ◽  
Qsar Modelling ◽  
Quantitative Structure Property Relationships

Topological indices are quantitative measurements that describe a molecule’s topology and are quantified from the molecule’s graphical representation. The significance of topological indices is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between a particular molecular or biological activity and one or several biochemical and/or molecular structural features are QSPRs (quantitative structure-property relationships) and QSARs (quantitative structure-activity relationships). In this paper, we give explicit expressions of two recently defined novel ev-degree- and ve-degree-based topological indices of two classes of benzenoid, namely, linear hexagonal chain and hammer-like benzenoid.

scholarly journals On Eccentricity-Based Topological Indices and Polynomials of Phosphorus Containing Dendrimers

2018 ◽  
Author(s):  
Shin Min Kang ◽  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Rabia Sarfraz ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
The Other ◽  
Topological Descriptors ◽  
Eccentric Connectivity Index ◽  
Important Place ◽  
Eccentricity Index ◽  
Phosphorus Containing ◽  
Pharmaceutical Properties ◽  
High Degree

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

scholarly journals Computation of General Zagreb Index of Nanotubes Covered by C5 and C7

2020 ◽  
Vol 11 (1) ◽  
pp. 8001-8008
Keyword(s):  
Carbon Nanotubes ◽  
Connected Graph ◽  
Molecular Graph ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Chemical Bonds ◽  
Graph Invariant ◽  
Zagreb Index ◽  
Physical And Chemical ◽  
Simple Connected Graph

A molecular graph is hydrogen deleted simple connected graph in which vertices and edges are represented by atoms and chemical bonds, respectively. Topological indices are numerical parameters of a molecular graph which characterize its topology and are usually graph invariant. In Mathematical chemistry, topological descriptors play an important role in modeling different physical and chemical activities of molecules. In this study, the generalized Zagreb index for three types of carbon nanotubes is computed. By putting some particular values to the parameters, some important degree-based topological indices are also derived.

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.

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