scholarly journals On the Degree-Based Topological Indices of Some Derived Networks

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 612 ◽  
Author(s):  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Muhammad Kashif Shafiq ◽  
Wei Gao
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Zagreb Index ◽  
Entire Structure ◽  
Physical Chemical ◽  
Chemical Descriptors

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.

Topological characterization of dendrimer, benzenoid, and nanocone

2018 ◽  
Vol 74 (1-2) ◽  
pp. 35-43
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Najma Abdul Rehman ◽  
Mehwish Hussain Muhammad
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Complex Molecules ◽  
Chemical Structures ◽  
Physico Chemical ◽  
Quantitative Structure Activity Relationships

Abstract Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

scholarly journals Computing Some Degree-Based Topological Indices of Honeycomb Networks

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-13
Author(s):  
Lili Gu ◽  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti ◽  
Peng Xu ◽  
Adnan Aslam
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Substance ◽  
Topological Indices ◽  
Connectivity Index ◽  
Silicate Network ◽  
Zagreb Index ◽  
First Order ◽  
Second Zagreb Index ◽  
Chain Silicate

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

scholarly journals Topological Characterization of Nanosheet Covered by C3 and C6

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 462
Author(s):  
Sumiya Nasir ◽  
Fozia Bashir Farooq ◽  
Nazeran Idrees ◽  
Muhammad Jawwad Saif ◽  
Fatima Saeed
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Physical And Chemical ◽  
Atom Bond ◽  
And Chemical Properties

A topological index of a graph is a single numeric quantity which relates the chemical structure with its underlying physical and chemical properties. Topological indices of a nanosheet can help us to understand the properties of the material better. This study deals with computation of degree-dependent topological indices like the Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper Zagreb index of nanosheet covered by C3 and C6. Furthermore, M-polynomial of the nanosheet is also computed, which provides an alternate way to express the topological indices.

scholarly journals The Wiener and Zagreb Indices of Conjugacy Class Graph of the Dihedral Groups

MATEMATIKA ◽  
2019 ◽  
Vol 35 (1) ◽  
pp. 51-57 ◽  
Author(s):  
Nur Idayu Alimon ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Conjugacy Class ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
Dihedral Groups ◽  
Zagreb Index ◽  
Vertex Set ◽  
Class Graph ◽  
The First Zagreb Index ◽  
Group Of Symmetries

Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of  is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order  where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups.  In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.

scholarly journals Topological Indices of mth Chain Silicate Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 42 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Kashif Shafiq ◽  
Haidar Ali ◽  
Asim Naseem ◽  
Nayab Maryam ◽  
...  
Keyword(s):  
Biological Activity ◽  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Numerical Representation ◽  
Topological Descriptor ◽  
Physico Chemical ◽  
Chain Silicate ◽  
Atom Bond

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, and biological activity are determined by the chemical applications of graph theory. The biological activity of chemical compounds can be constructed by the help of topological indices such as atom-bond connectivity (ABC), Randić, and geometric arithmetic (GA). In this paper, Randić, atom bond connectivity (ABC), Zagreb, geometric arithmetic (GA), ABC4, and GA5 indices of the mth chain silicate S L ( m , n ) network are determined.

scholarly journals On Topological Indices of mth Chain Hex-Derived Network of Third Type

2020 ◽  
Vol 8 ◽  
Author(s):  
Yuhong Huo ◽  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Syed Sheraz Asghar ◽  
Usman Babar ◽  
...  
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Vaporization Enthalpy ◽  
Graphical View ◽  
Type 3 ◽  
Physical And Chemical ◽  
Atom Bond ◽  
And Chemical Properties

In theoretical chemistry, the numerical parameters that are used to characterize the molecular topology of graphs are called topological indices. Several physical and chemical properties like boiling point, entropy, heat formation, and vaporization enthalpy of chemical compounds can be determined through these topological indices. Graph theory has a considerable use in evaluating the relation of various topological indices of some derived graphs. In this article, we will compute the topological indices like Randić, first Zagreb, harmonic, augmented Zagreb, atom-bond connectivity, and geometric-arithmetic indices for chain hex-derived network of type 3 CHDN3(m,n) for different cases of m and n. We will also compute the numerical computation and graphical view to justify our results.Mathematics Subject Classification: 05C12, 05C90

scholarly journals A Computational Approach on Acetaminophen Drug using Degree-Based Topological Indices and M-Polynomials

2021 ◽  
Vol 12 (6) ◽  
pp. 7249-7266
Keyword(s):  
Biological Activity ◽  
Physicochemical Properties ◽  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Chemical Compounds ◽  
Computational Approach ◽  
Topological Indices ◽  
Numerical Representation ◽  
Essential Drug

Topological index is a numerical representation of a chemical structure. Based on these indices, physicochemical properties, thermodynamic behavior, chemical reactivity, and biological activity of chemical compounds are calculated. Acetaminophen is an essential drug to prevent/treat various types of viral fever, including malaria, flu, dengue, SARS, and even COVID-19. This paper computes the sum and multiplicative version of various topological indices such as General Zagreb, General Randić, General OGA, AG, ISI, SDD, Forgotten indices M-polynomials of Acetaminophen. To the best of our knowledge, for the Acetaminophen drugs, these indices have not been computed previously.

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

Chemical structure and physical-chemical properties of mucilage from the leaves of Pereskia aculeata

2017 ◽  
Vol 70 ◽  
pp. 20-28 ◽  
Author(s):  
Andressa Amado Martin ◽  
Rilton Alves de Freitas ◽  
Guilherme Lanzi Sassaki ◽  
Paulo Henrique Labiak Evangelista ◽  
Maria Rita Sierakowski
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Physical Chemical

TOPOLOGICAL INDICES – WHY AND HOW

2021 ◽  
Author(s):  
Ivan Gutman ◽  
Keyword(s):  
Single Molecule ◽  
Chemical Structure ◽  
Chemical Reactivity ◽  
Chemical Species ◽  
Chemical Compounds ◽  
Simple Calculation ◽  
Topological Indices ◽  
High Level ◽  
Complex Phenomena ◽  
Real World Problems

By means of presently available high-level computational methods, based on quantum theory, it is possible to determine (predict) the main structural, electronic, energetic, geometric, and thermodynamic properties of a particular chemical species (usually a molecule), as well as the ways in which it changes in chemical reactions. When one needs to estimate such properties of thousands or millions of chemical species, such high-level calculations are no more feasible. Then simpler, but less accurate, approaches are necessary. One such approach utilized so-called “topological indices”. According to IUPAC ‘s definition [Pure Appl. Chem. 69 (1997) 1137]: A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In the first part of the lecture, we show that „numerical values“are associated with many other complex phenomena, encountered in various areas of human activity, implying that „topological indices“ are used far beyond chemistry. Next, we discuss the number of possible chemical compounds. Simple calculation shows that the number of possible compounds zillion times exceeds the number of those that have been experimentally characterized. Even worse, in the entire Universe, there is not enough matter to make at least a single molecule of each possible compound. In the second part of the lecture, a few most popular topological indices will be presented, as well as the way in which these can be (and are being) applied in treating real-world problems.

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