On Certain Topological Indices of Three-Layered Single-Walled Titania Nanosheets

2020 ◽  
Vol 23 ◽  
Author(s):  
Micheal Arockiaraj ◽  
Jia-Bao Liu ◽  
M. Arulperumjothi ◽  
S. Prabhu
Keyword(s):  
Materials Science ◽  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Mathematical Properties ◽  
Chemical Graph Theory ◽  
Research Article ◽  
Cut Method

Aim and Objective: Nanostructures are objects whose sizes are between microscopic and molecular. The most significant of these new elements are carbon nanotubes. These elements have extraordinary microelectronic properties and many other exclusive physiognomies. Recently, researchers have given the attention to the mathematical properties of these materials. The aim and objective of this research article is to investigate the most important molecular descriptors namely Wiener, edge-Wiener, vertex-edge-Wiener, vertex-Szeged, edge-Szeged, edge-vertex-Szeged, total-Szeged, PI, Schultz, Gutman, Mostar, edge-Mostar, and total-Mostar indices of three-layered single-walled titania nanosheets. By computing these topological indices, materials science researchers can have a better understanding of structural and physical properties of titania nanosheets, and thereby more easily synthesizing new variants of titania nanosheets with more amenable physicochemical properties. Methods: The cut method turned out to be extremely handy when dealing with distance-based graph invariants which are in turn among the central concepts of chemical graph theory. In this method, we use the Djokovic ́-Winkler relation to find the suitable edge cuts to leave the graph into exactly two components. Based on the graph theoretical measures of the components, we obtain the desired topological indices by mathematical computations. Results: In this paper, distance-based indices for three-layered single-walled titania nanosheets were investigated and given the exact expressions for various dimensions of three-layered single-walled titania nanosheets. These indices may be useful in synthesizing new variants of titania nanosheets and the computed topological indices play an important role in studies of Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR). Conclusion: In this paper, we have obtained the closed expressions of several distance-based topological indices of three-layered single-walled titania nanosheet TNS_3 [m,n] molecular graph for the cases m≥ n and m < n. The graphical validations for the computed indices are done and we observe that the Wiener types, Schultz and Gutman indices perform in a similar way whereas PI and Mostar type indices perform in the same way.

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 On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

2022 ◽  
Vol 19 (2) ◽  
pp. 2022
Author(s):  
Tapan Kumar Baishya ◽  
Bijit Bora ◽  
Pawan Chetri ◽  
Upashana Gogoi
Keyword(s):  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Three Dimensions ◽  
Topological Descriptors ◽  
Quantitative Structure ◽  
Structure Property ◽  
Physiochemical Properties ◽  
3 Dimensional ◽  
Structure Property Relationship

Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively. HIGHLIGHTS Calculated degree based Topological indices of a 3D crystal from M-polynomial A relation among various Topological indices is established geometrically Variations of Topological Indices along three dimensions (directions) are shown geometrically Harmonic index approximates the degree variation of oxygen atom

scholarly journals The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

2021 ◽  
pp. 54-75
Author(s):  
Mohammed Alsharafi ◽  
Yusuf Zeren ◽  
Abdu Alameri
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Strong Product ◽  
Chemical Graph Theory ◽  
Mathematical Operations

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

scholarly journals On Knowledge Discovery and Representations of Molecular Structures Using Topological Indices

2021 ◽  
Vol 11 (1) ◽  
pp. 21-32
Author(s):  
Fawaz E. Alsaadi ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Aqsa Shah ◽  
Usman Ali ◽  
Jinde Cao ◽  
...  
Keyword(s):  
Topological Index ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Graph Automorphism ◽  
Structure Property Relationship ◽  
Atom Bond

AbstractThe main purpose of a topological index is to encode a chemical structure by a number. A topological index is a graph invariant, which decribes the topology of the graph and remains constant under a graph automorphism. Topological indices play a wide role in the study of QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship). Topological indices are implemented to judge the bioactivity of chemical compounds. In this article, we compute the ABC (atom-bond connectivity); ABC4 (fourth version of ABC), GA (geometric arithmetic) and GA5 (fifth version of GA) indices of some networks sheet. These networks include: octonano window sheet; equilateral triangular tetra sheet; rectangular sheet; and rectangular tetra sheet networks.

scholarly journals Bounds for the Topological Indices of ℘ graph

2021 ◽  
Vol 14 (2) ◽  
pp. 340-350
Author(s):  
Muddalapuram Manjunath ◽  
V. Lokesha ◽  
. Suvarna ◽  
Sushmitha Jain
Keyword(s):  
Finite Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Lower And Upper Bounds ◽  
Zagreb Index ◽  
Chemical Structures ◽  
Structure Property Relationship ◽  
Atom Bond

Topological indices are mathematical measure which correlates to the chemical structures of any simple finite graph. These are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR). In this paper, we define operator graph namely, ℘ graph and structured properties. Also, establish the lower and upper bounds for few topological indices namely, Inverse sum indeg index, Geometric-Arithmetic index, Atom-bond connectivity index, first zagreb index and first reformulated Zagreb index of ℘-graph.

scholarly journals ON CERTAIN TOPOLOGICAL INDICES OF BENZENOID COMPOUNDS

2017 ◽  
Vol 13 (8) ◽  
pp. 6406-6412 ◽  
Author(s):  
S. Prabhu ◽  
M. Arulperumjothi
Keyword(s):  
Drug Design ◽  
Molecular Graph ◽  
Topological Indices ◽  
Rational Drug Design ◽  
Quantitative Structure ◽  
Structure Property ◽  
Molecular Graphics ◽  
Structural Graph ◽  
Rational Drug ◽  
Quantitative Structure Property Relationships

Drug discovery is mainly the result of chance discovery and massive screening of large corporate libraries of synthesized or naturally-occurring compounds. Computer aided drug design is an approach to rational drug design made possible by the recent advances in computational chemistry in various fields of chemistry, such as molecular graphics, molecular mechanics, quantum chemistry, molecular dynamics, library searching, prediction of physical, chemical, and biological properties.  The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. Topological indices are designed basically by transforming a molecular graph into a number. A topological index is a numeric quantity of a molecule that is mathematically derived from the structural graph of a molecule. In this paper we compute certain topological indices of pyrene molecular graph. The topological indices are used in quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) studies. 

On Certain Counting Polynomial of Titanium Dioxide Nanotubes

2019 ◽  
Vol 9 (2) ◽  
pp. 240-243 ◽  
Author(s):  
S. Prabhu ◽  
M. Arulperumjothi ◽  
G. Murugan ◽  
V.M. Dhinesh ◽  
J.P. Kumar
Keyword(s):  
Biological Activities ◽  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Vital Role ◽  
Quantitative Structure ◽  
Structure Property ◽  
Covalent Bonds ◽  
Mathematical Chemistry ◽  
Topological Description ◽  
Counting Polynomial

Background: In 1936, Polya introduced the concept of a counting polynomial in chemistry. However, the subject established little attention from chemists for some decades even though the spectra of the characteristic polynomial of graphs were considered extensively by numerical means in order to obtain the molecular orbitals of unsaturated hydrocarbons. Counting polynomial is a sequence representation of a topological stuff so that the exponents precise the magnitude of its partitions while the coefficients are correlated to the occurrence of these partitions. Counting polynomials play a vital role in topological description of bipartite structures as well as counts of equidistant and non-equidistant edges in graphs. Omega, Sadhana, PI polynomials are wide examples of counting polynomials. Methods: Mathematical chemistry is a division of abstract chemistry in which we debate and forecast the chemical structure by using mathematical models. Chemical graph theory is a subdivision of mathematical chemistry in which the structure of a chemical compound can be embodied by a labelled graph whose vertices are atoms and edges are covalent bonds between the atoms. We use graph theoretic technique in finding the counting polynomials of TiO2 nanotubes. : Let ! be the molecular graph of TiO2. Then (!, !) = !!10!!+8!−2!−2 + (2! +1) !10!!+8!−2! + 2(! + 1)10!!+8!−2 Results: In this paper, the omega, Sadhana and PI counting polynomials are studied. These polynomials are useful in determining the omega, Sadhana and PI topological indices which play an important role in studies of Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR) which are used to predict the biological activities and properties of chemical compounds. Conclusion: These counting polynomials play an important role in topological description of bipartite structures as well as counts equidistance and non-equidistance edges in graphs. Computing distancecounting polynomial is under investigation.

scholarly journals On Topological Indices for New Classes of Benes Network

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Aftab Hussain ◽  
Muhammad Numan ◽  
Nafisa Naz ◽  
Saad Ihsan Butt ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Structure Property ◽  
Structure Activity ◽  
Randić Connectivity Index ◽  
Structure Property Relationship ◽  
Benes Network ◽  
Benes Networks ◽  
Atom Bond

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

scholarly journals Computation of certain topological coindices of graphene sheet and C4C8(S) nanotubes and nanotorus

2019 ◽  
Vol 4 (2) ◽  
pp. 455-468 ◽  
Author(s):  
Melaku Berhe ◽  
Chunxiang Wang
Keyword(s):  
Graphene Sheet ◽  
Biological Activities ◽  
Chemical Properties ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Relationship Of ◽  
The Relationship

AbstractTopological indices are widely used for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). Topological coindices are topological indices that considers the non adjacent pairs of vertices. Here, we consider the following five well-known topological coindices: the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices and the F-coindex. By using graph structural analysis and derivation, we study the above-mentioned topological coindices of some chemical molecular graphs that frequently appear in medical, chemical, and material engineering such as graphene sheet and C4C8(S) nanotubes and nanotorus and obtain the computation formulae of the coindices of these graphs. Furthermore, we analyze the results by MATLAB and obtain the relationship of the coindices which they describe the physcio-chemical properties and biological activities.

scholarly journals On multiplicative degree based topological indices for planar octahedron networks

2020 ◽  
Vol 43 (1) ◽  
pp. 219-228
Author(s):  
Ghulam Dustigeer ◽  
Haidar Ali ◽  
Muhammad Imran Khan ◽  
Yu-Ming Chu
Keyword(s):  
Graph Theory ◽  
Information Science ◽  
Biological Activities ◽  
Molecular Graph ◽  
Triangular Prism ◽  
Structure Property ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Chemical Graph Theory ◽  
Analytical Formulas

AbstractChemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is at least one connection between its vertices. The number that describes the topology of the graph is called the topological index. Cheminformatics is a new subject which is a combination of chemistry, mathematics and information science. It studies quantitative structure-activity (QSAR) and structure-property (QSPR) relationships that are used to predict the biological activities and properties of chemical compounds. We evaluated the second multiplicative Zagreb index, first and second universal Zagreb indices, first and second hyper Zagreb indices, sum and product connectivity indices for the planar octahedron network, triangular prism network, hex planar octahedron network, and give these indices closed analytical formulas.

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