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

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 .

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Topological Characterization of Nanosheet Covered by C3 and C6

Processes ◽

10.3390/pr7070462 ◽

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.

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Some degree-based topological indices of caboxy-terminated dendritic macromolecule

Main Group Metal Chemistry ◽

10.1515/mgmc-2021-0016 ◽

2021 ◽

Vol 44 (1) ◽

pp. 165-172

Author(s):

Yongsheng Rao ◽

Ammarah Kanwal ◽

Riffat Abbas ◽

Saima Noureen ◽

Asfand Fahad ◽

...

Keyword(s):

Graph Theory ◽

Chemical Properties ◽

Biochemical Properties ◽

Topological Indices ◽

Connectivity Index ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Modern Era ◽

Dendritic Macromolecule ◽

Atom Bond

Abstract In the modern era of the chemical science, the chemical graph theory has contributed significantly to exploring the properties of the chemical compounds. Currently, the computation of the topological indices is one of the most active directions of the research in the area of the chemical graph theory. The main feature of the study of the topological indices is its its ability of predicting the various physio-chemical properties. In this article, we compute several degree-based topological indices for the caboxy-terminated dendritic macromolecule. We compute Harmonic index, atom-bond connectivity index, geometric arithmetic index, sum connectivity index, inverse sum index, symmetric division degree, and Zagreb indices for caboxy-terminated dendritic macromolecule. The obtained results have potential to predict biochemical properties such as viscosity, entropy, and boiling point.

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

Frontiers in Physics ◽

10.3389/fphy.2020.593275 ◽

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

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On eccentricity-based topological descriptors of water-soluble dendrimers

Zeitschrift für Naturforschung C ◽

10.1515/znc-2018-0123 ◽

2018 ◽

Vol 74 (1-2) ◽

pp. 25-33 ◽

Cited By ~ 11

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.

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Topological aspects of some dendrimer structures

Nanotechnology Reviews ◽

10.1515/ntrev-2017-0184 ◽

2018 ◽

Vol 7 (2) ◽

pp. 123-129 ◽

Cited By ~ 14

Author(s):

Adnan Aslam ◽

Muhammad Kamran Jamil ◽

Wei Gao ◽

Waqas Nazeer

Keyword(s):

Self Assembly ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Connectivity Index ◽

Molecular Topology ◽

Zinc Porphyrin ◽

Physico Chemical ◽

Randić Connectivity Index ◽

Atom Bond

AbstractA numerical number associated to the molecular graphGthat describes its molecular topology is called topological index. In the study ofQSARandQSPR, topological indices such as atom-bond connectivity index, Randić connectivity index, geometric index, etc. help to predict many physico-chemical properties of the chemical compound under study. Dendrimers are macromolecules and have many applications in chemistry, especially in self-assembly procedures and host-guest reactions. The aim of this report is to compute degree-based topological indices, namely the fourth atom-bond connectivity index and fifth geometric arithmetic index of poly propyl ether imine, zinc porphyrin, and porphyrin dendrimers.

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Computing Some Degree-Based Topological Indices of Honeycomb Networks

Complexity ◽

10.1155/2022/2771059 ◽

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 .

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Topological Indices of Certain Transformed Chemical Structures

Journal of Chemistry ◽

10.1155/2020/3045646 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xuewu Zuo ◽

Jia-Bao Liu ◽

Hifza Iqbal ◽

Kashif Ali ◽

Syed Tahir Raza Rizvi

Keyword(s):

Carbon Nanotube ◽

Line Graph ◽

Topological Indices ◽

Connectivity Index ◽

Zagreb Index ◽

Harmonic Index ◽

Chemical Structures ◽

Augmented Zagreb Index ◽

Carbon Nanotube Networks ◽

Atom Bond

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

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Edge Version Molecular Descriptors of Tetrameric 1, 3 Adamantane

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.10.21026 ◽

2018 ◽

Vol 7 (4.10) ◽

pp. 403

Author(s):

G. Mohanappriya ◽

D. Vijiyalakshmi

Keyword(s):

Molecular Descriptors ◽

Molecular Graph ◽

Topological Indices ◽

Connectivity Index ◽

Zagreb Index ◽

Numerical Invariants ◽

Atom Bond

Molecular descriptors (Topological indices) are the numerical invariants of a molecular graph which distinguish its topology. In this article, we compute edge version of topological indices such as Zagreb index, Atom bond connectivity index, Fourth atom bond connectivity index, Geometric Arithmetic index and Fifth Geometric Arithmetic index of tetrameric 1,3 adamantane.

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Topological Indices of Some New Graph Operations and Their Possible Applications

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v13i230302 ◽

2021 ◽

pp. 16-30

Author(s):

Abdu Qaid Saif Alameri ◽

Mohammed Saad Yahya Al-Sharafi

Keyword(s):

Graph Theory ◽

Chemical Compounds ◽

Topological Indices ◽

First Zagreb Index ◽

Zagreb Index ◽

Structural Invariant ◽

Graph Operations ◽

Chemical Graph Theory ◽

Cyclic Alkanes ◽

The First Zagreb Index

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

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On molecular topological properties of benzenoid structures

Canadian Journal of Chemistry ◽

10.1139/cjc-2016-0032 ◽

2016 ◽

Vol 94 (8) ◽

pp. 687-698 ◽

Cited By ~ 8

Author(s):

Shehnaz Akhter ◽

Muhammad Imran

Keyword(s):

Strain Energy ◽

Chemical Compounds ◽

Topological Indices ◽

Connectivity Index ◽

Line Graphs ◽

Zigzag Edge ◽

Zagreb Index ◽

Chemical Significance ◽

Randić Connectivity Index ◽

Atom Bond

The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most important due to their chemical significance. In this paper, we compute the first general Zagreb index, general Randić connectivity index, general sum-connectivity index, ABC, GA, ABC4, and GA5 indices of hexagonal parallelogram P(m,n) nanotubes, triangular benzenoid Gn, and zigzag-edge coronoid fused with starphene ZCS(k,l,m) nanotubes by using the line graphs of the subdivision of these chemical graphs.

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