scholarly journals Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Muhammad Javaid ◽  
Saira Javed ◽  
Yasmene F. Alanazi ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Lexicographic Product ◽  
Statistical Tools ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Molecule Structure ◽  
Polygonal Chains ◽  
Computing Correlation ◽  
And Chemical Properties

A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.

Graph Indices for Cartesian Product of F-sum of Connected Graphs

2021 ◽  
Vol 24 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Imran ◽  
Shakila Baby ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Kashif Shafiq
Keyword(s):  
Computer Science ◽  
Topological Index ◽  
Cartesian Product ◽  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Finite Graphs ◽  
Zagreb Indices ◽  
Physical And Chemical ◽  
Minimum Degrees ◽  
And Chemical Properties

Background: A topological index is a real number associated to a graph, that provides information about its physical and chemical properties along with their correlations.Topological indices are being used successfully in Chemistry, Computer Science and many other fields. Aim and Objective: In this article, we apply the well known, Cartesian product on F-sums of connected and finite graphs. We formulate sharp limits for some famous degree dependent indies. Results: Zagreb indices for the graph operations T(G), Q(G), S(G), R(G) and their F-sums have been computed. By using orders and sizes of component graphs, we derive bounds for Zagreb indices, F-index and Narumi-Katayana index. Conclusion: The formulation of expressions for the complicated products on F-sums, in terms of simple parameters like maximum and minimum degrees of basic graphs, reduces the computational complexities.

scholarly journals Zagreb Polynomials and Redefined Zagreb Indices for Chemical Structures Helpful in the Treatment of COVID-19

2020 ◽  
Vol 4 (4) ◽  
pp. 33-40
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index (TI) is a number that is helpful in predicting the properties of chemical compounds. We can estimate the physical and chemical properties of several chemical compounds. In this study, we compute Zagreb polynomials and the redefined Zagreb indices for chemical compounds used in the treatment of COVID-19 namely remdesivir, chloroquine, hydroxychloroquine and theaflavin.

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-Polynomials and Associated Topological Indices of Sodalite Materials

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ghazanfar Abbas ◽  
Muhammad Ibrahim ◽  
Ali Ahmad ◽  
Muhammad Azeem ◽  
Kashif Elahi
Keyword(s):  
Greenhouse Gases ◽  
Topological Index ◽  
Low Cost ◽  
Chemical Properties ◽  
Topological Indices ◽  
Mathematical Tool ◽  
Physical And Chemical Properties ◽  
Natural Zeolites ◽  
Physical And Chemical ◽  
And Chemical Properties

Natural zeolites are commonly described as macromolecular sieves. Zeolite networks are very trendy chemical networks due to their low-cost implementation. Sodalite network is one of the most studied types of zeolite networks. It helps in the removal of greenhouse gases. To study this rich network, we use an authentic mathematical tool known as M-polynomials of the topological index and show some physical and chemical properties in numerical form, and to understand the structure deeply, we compare different legitimate M-polynomials of topological indices, concluding in the form of graphical comparisons.

ON THE WIENER INDEX OF F_H SUMS OF GRAPHS

2021 ◽  
Vol 3 (2) ◽  
pp. 37-57
Author(s):  
L. Alex ◽  
Indulal G
Keyword(s):  
Complete Graph ◽  
Cartesian Product ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
Single Vertex ◽  
Molecular Graphs ◽  
New Class ◽  
And Chemical Properties

Wiener index is the first among the long list of topological indices which was used to correlate structural and chemical properties of molecular graphs. In \cite{Eli} M. Eliasi, B. Taeri defined four new sums of graphs based on the subdivision of edges with regard to the cartesian product and computed their Wiener index. In this paper, we define a new class of sums called $F_H$ sums and compute the Wiener index of the resulting graph in terms of the Wiener indices of the component graphs so that the results in \cite{Eli} becomes a particular case of the Wiener index of $F_H$ sums for $H = K_1$, the complete graph on a single vertex.

scholarly journals An Introductory Note on the Spectrum and Energy of Molecular Graphs

2017 ◽  
Vol 16 (2) ◽  
pp. 17-27
Author(s):  
Ann Susa Thomas ◽  
Sunny Joseph Kalayathankal ◽  
Joseph Varghese Kureethara
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Structural Studies ◽  
Theoretical Methods ◽  
Molecular Graphs ◽  
Introductory Note ◽  
Introductory Paper ◽  
Physical And Chemical ◽  
And Chemical Properties

Graph Theory is one branch of Mathematics that laid the foundations of the structural studies in Chemistry. The fact that every molecule or compound can be represented as a network of vertices (elements) and edges (bonds) provoked the question of the predictability of the physical and chemical properties of molecules and compounds. Spectrum, π-electron energy, Spectral Radius etc. are predictable using graph theoretical methods. This is an introductory paper about spectrum and energy of molecular graphs.

Extremal (n,m)-Graphs w.r.t General Multiplicative Zagreb Indices

2020 ◽  
Vol 23 ◽  
Author(s):  
Aisha Javed ◽  
Muhammad Kamran Jamil ◽  
Jia-Bao Liu ◽  
Akbar Ali
Keyword(s):  
Molecular Graph ◽  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Extremal Graphs ◽  
Unified Approach ◽  
Zagreb Indices ◽  
Graph Transformations ◽  
Bicyclic Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Background:: A topological index of a molecular graph is the numeric quantity which can predict certain physical and chemical properties of the corresponding molecule. Xu et al. introduced some graph transformations which increase or decrease the first and second multiplicative Zagreb indices and proposed a unified approach to characterize extremal (n, m)- graphs. Method:: Graph transformations are used to find the extremal graphs, these transformations either increase or decrease the general multiplicative Zagreb indices. By applying the transformations which increase the general multiplicative Zagreb indices we find the graphs with maximal general multiplicative Zagreb indices and for minimal general Zagreb indices we use the transformations which decrease the index. Result:: In this paper, we extend the Xu’s results and show that the same graph transformations increase or decrease the first and second general multiplicative Zagreb indices for . As an application, the extremal acyclic, unicyclic and bicyclic graphs are presented for general multiplicative Zagreb indices. Conclusion:: By applying the transformation we investigated that in the class of acyclic, unicyclic and bicyclic graphs, which graph gives the minimum and the maximum general multiplicative Zagreb indices.

scholarly journals F-Index of some graph operations

2016 ◽  
Vol 08 (02) ◽  
pp. 1650025 ◽  
Author(s):  
Nilanjan De ◽  
Sk. Md. Abu Nayeem ◽  
Anita Pal
Keyword(s):  
Electron Energy ◽  
Topological Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Basic Properties ◽  
Graph Operations ◽  
Physico Chemical ◽  
Vertex Degrees

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total [Formula: see text]-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [A forgotten topological index,J. Math. Chem. 53(4) (2015) 1184–1190.] reinvestigated the index and named it “forgotten topological index” or “F-index”. In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nanostructures.

scholarly journals Some Topological Measures for Nicotine

2020 ◽  
pp. 287-296
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Topological Measures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index is a quantity expressed as a number that help us to catch symmetry of chemical compounds. With the help of quantitative structure property relationship (QSPR), we can guess physical and chemical properties of several chemical compounds. Here, we will compute Shingali & Kanabour, Gourava and hype Gourava indices for the chemical compound Nicotine.

scholarly journals Molecular Properties of Symmetrical Networks Using Topological Polynomials

2019 ◽  
Vol 17 (1) ◽  
pp. 849-864 ◽  
Author(s):  
Xing-Long Wang ◽  
Jia-Bao Liu ◽  
Maqsood Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Hussain ◽  
...  
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Chemical Species ◽  
Chemical Properties ◽  
Biological Properties ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Physico Chemical ◽  
Symmetry Properties ◽  
Physical Features

AbstractA numeric quantity that comprehend characteristics of molecular graph Γ of chemical compound is known as topological index. This number is, in fact, invariant with respect to symmetry properties of molecular graph Γ. Many researchers have established, after diverse studies, a parallel between the physico chemical properties like boiling point, stability, similarity, chirality and melting point of chemical species and corresponding chemical graph. These descriptors defined on chemical graphs are extremely helpful for researchers to conduct regression model like QSAR/QSPR and better understand the physical features, complexity of molecules, chemical and biological properties of underlying compound.In this paper, several structure descriptors of vital importance, namely, first, second, modified and augmented Zagreb indices, inverse and general Randic indices, symmetric division, harmonic, inverse sum and forgotten indices of Hex-derived Meshes (networks) of two kinds, namely, HDN1(n) and HDN2(n) are computed and recovered using general approach of topological polynomials.

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