scholarly journals Computing Analysis of Zagreb Indices for Generalized Sum Graphs under Strong Product

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Muhammad Javaid ◽  
Saira Javed ◽  
Abdulaziz Mohammed Alanazi ◽  
Majdah R. Alotaibi
Keyword(s):  
Chemical Engineering ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Vital Role ◽  
Molecular Structures ◽  
Zagreb Indices ◽  
Graph Theoretic ◽  
Strong Product ◽  
Physicochemical And Structural Properties ◽  
Product Of Graphs

Numerous studies based on mathematical models and tools indicate that there is a strong inherent relationship between the chemical properties of the chemical compounds and drugs with their molecular structures. In the last two decades, the graph-theoretic techniques are frequently used to analyse the various physicochemical and structural properties of the molecular graphs which play a vital role in chemical engineering and pharmaceutical industry. In this paper, we compute Zagreb indices of the generalized sum graphs in the form of the different indices of their factor graphs, where generalized sum graphs are obtained under the operations of subdivision and strong product of graphs. Moreover, the obtained results are illustrated with the help of particular classes of graphs and analysed to find the efficient subclass with dominant indices.

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 Computing Bounds for Second Zagreb Coindex of Sum Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Javaid ◽  
Muhammad Ibraheem ◽  
Uzma Ahmad ◽  
Q. Zhu
Keyword(s):  
Computer Science ◽  
Cartesian Product ◽  
Chemical Properties ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Graph Theoretic ◽  
Cartesian Product Of Graphs ◽  
The Subject ◽  
Product Of Graphs ◽  
And Chemical Properties

Topological indices or coindices are one of the graph-theoretic tools which are widely used to study the different structural and chemical properties of the under study networks or graphs in the subject of computer science and chemistry, respectively. For these investigations, the operations of graphs always played an important role for the study of the complex networks under the various topological indices or coindices. In this paper, we determine bounds for the second Zagreb coindex of a well-known family of graphs called F -sum ( S -sum, R -sum, Q -sum, and T -sum) graphs in the form of Zagreb indices and coindices of their factor graphs, where these graphs are obtained by using four subdivision-related operations and Cartesian product of graphs. At the end, we illustrate the obtained results by providing the exact and bonded values of some specific F -sum graphs.

scholarly journals Multiplicative Zagreb Indices of Molecular Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Xiujun Zhang ◽  
H. M. Awais ◽  
M. Javaid ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Mathematical Modeling ◽  
Vital Role ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Structure Properties

Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.

scholarly journals Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Jia-Bao Liu ◽  
Sana Akram ◽  
Muhammad Javaid ◽  
Zhi-Ba Peng
Keyword(s):  
Structural Properties ◽  
Crucial Role ◽  
Chemical Compounds ◽  
Molecular Networks ◽  
Lexicographic Product ◽  
Zagreb Indices ◽  
Physicochemical And Structural Properties

The use of numerical numbers to represent molecular networks plays a crucial role in the study of physicochemical and structural properties of the chemical compounds. For some integer k and a network G , the networks S k G and R k G are its derived networks called as generalized subdivided and generalized semitotal point networks, where S k and R k are generalized subdivision and generalized semitotal point operations, respectively. Moreover, for two connected networks, G 1 and G 2 , G 1 G 2 S k and G 1 G 2 R k are T -sum networks which are obtained by the lexicographic product of T G 1 and G 2 , respectively, where T ε S k , R k . In this paper, for the integral value k ≥ 1 , we find exact values of the first and second Zagreb indices for generalized T -sum networks. Furthermore, the obtained findings are general extensions of some known results for only k = 1 . At the end, a comparison among the different generalized T -sum networks with respect to first and second Zagreb indices is also included.

scholarly journals Editorial: Topological investigations of chemical networks

2021 ◽  
Vol 44 (1) ◽  
pp. 267-269
Author(s):  
Muhammad Javaid ◽  
Muhammad Imran
Keyword(s):  
Information Science ◽  
Biological Activities ◽  
Chemical Properties ◽  
Vital Role ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Chemical Structures ◽  
Interdisciplinary Field

Abstract The topic of computing the topological indices (TIs) being a graph-theoretic modeling of the networks or discrete structures has become an important area of research nowadays because of its immense applications in various branches of the applied sciences. TIs have played a vital role in mathematical chemistry since the pioneering work of famous chemist Harry Wiener in 1947. However, in recent years, their capability and popularity has increased significantly because of the findings of the different physical and chemical investigations in the various chemical networks and the structures arising from the drug designs. In additions, TIs are also frequently used to study the quantitative structure property relationships (QSPRs) and quantitative structure activity relationships (QSARs) models which correlate the chemical structures with their physio-chemical properties and biological activities in a dataset of chemicals. These models are very important and useful for the research community working in the wider area of cheminformatics which is an interdisciplinary field combining mathematics, chemistry, and information science. The aim of this editorial is to arrange new methods, techniques, models, and algorithms to study the various theoretical and computational aspects of the different types of these topological indices for the various molecular structures.

scholarly journals Computing FGZ Index of Sum Graphs under Strong Product

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhi-Ba Peng ◽  
Saira Javed ◽  
Muhammad Javaid ◽  
Jia-Bao Liu
Keyword(s):  
Structural Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Zagreb Index ◽  
Strong Product ◽  
Product Of Graphs

Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related operations and strong product of graphs which create hexagonal chains isomorphic to many chemical compounds. Mainly, the exact values of first general Zagreb index (FGZI) for four sum graphs are obtained. At the end, FGZI of the two particular families of sum graphs are also computed as applications of the main results. Moreover, the dominating role of the FGZI among these sum graphs is also shown using the numerical values and their graphical presentations.

scholarly journals Topological Characterizations and Index-Analysis of New Degree-Based Descriptors of Honeycomb Networks

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 478 ◽  
Author(s):  
Zafar Hussain ◽  
Mobeen Munir ◽  
Shazia Rafique ◽  
Shin Min Kang
Keyword(s):  
Line Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Structures ◽  
Theoretic Analysis ◽  
Zagreb Index ◽  
Graph Theoretic ◽  
Index Analysis ◽  
First Time ◽  
Honeycomb Network

Topological indices and connectivity polynomials are invariants of molecular graphs. These invariants have the tendency of predicting the properties of the molecular structures. The honeycomb network structure is an important type of benzene network. In the present article, new topological characterizations of honeycomb networks are given in the form of degree-based descriptors. In particular, we compute Zagreb and Forgotten polynomials and some topological indices such as the hyper-Zagreb index, first and second multiple Zagreb indices and the Forgotten index, F. We, for the first time, determine some regularity indices such as the Albert index, Bell index and I R M ( G ) index, as well as the F-index of the complement of the honeycomb network and several co-indices related to this network without considering the graph of its complement or even the line graph. These indices are useful for correlating the physio-chemical properties of the honeycomb network. We also give a graph theoretic analysis of some indices against the dimension of this network.

scholarly journals Classification of Upper Bound Sequences of Local Fractional Metric Dimension of Rotationally Symmetric Hexagonal Planar Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Shahbaz Ali ◽  
Muhammad Khalid Mahmood ◽  
Fairouz Tchier ◽  
F. M. O. Tawfiq
Keyword(s):  
Image Processing ◽  
Chemical Engineering ◽  
Chemical Compounds ◽  
Vital Role ◽  
Metric Dimension ◽  
Integer Programming Problem ◽  
Rotationally Symmetric ◽  
Metric Dimensions ◽  
Planar Networks

The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequences of the local fractional metric dimensions of proposed rotationally symmetric and planar networks. Also, we discuss the boundedness of sequences of local fractional metric dimensions. Moreover, we summarize the sequences of local fractional metric dimension by means of their graphs.

scholarly journals M-Polynomials and Topological Indices of Dominating David Derived Networks

2018 ◽  
Vol 16 (1) ◽  
pp. 201-213 ◽  
Author(s):  
Shin Min Kang ◽  
Waqas Nazeer ◽  
Wei Gao ◽  
Deeba Afzal ◽  
Syeda Nausheen Gillani
Keyword(s):  
Biological Activity ◽  
Chemical Reactivity ◽  
Chemical Compounds ◽  
Strong Relationship ◽  
Topological Indices ◽  
Molecular Structures ◽  
Chemical Characteristics ◽  
Topological Properties ◽  
Zagreb Indices ◽  
Physical Features

AbstractThere is a strong relationship between the chemical characteristics of chemical compounds and their molecular structures. Topological indices are numerical values associated with the chemical molecular graphs that help to understand the physical features, chemical reactivity, and biological activity of chemical compound. Thus, the study of the topological indices is important. M-polynomial helps to recover many degree-based topological indices for example Zagreb indices, Randic index, symmetric division idex, inverse sum index etc. In this article we compute M-polynomials of dominating David derived networks of the first type, second type and third type of dimension n and find some topological properties by using these M-polynomials. The results are plotted using Maple to see the dependence of topological indices on the involved parameters.

Some valency oriented molecular invariants of certain networks.

2020 ◽  
Vol 23 ◽  
Author(s):  
Muhammad Salman ◽  
Faisal Ali ◽  
Masood Ur Rehman ◽  
Imran Khalid
Keyword(s):  
Molecular Structure ◽  
Boiling Point ◽  
Strain Energy ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
Atom Bond ◽  
Honeycomb Network ◽  
Silicate Sheet

Background: The valency of an atom in a molecular structure is the number of its neighboring atoms. A large number of valency based molecular invariants have been conceived, which correlate certain physio-chemical properties like boiling point, stability, strain energy and many more of chemical compounds. Objective: Our aim is to study the valency based molecular invariants for four hexa chemical structures, namely hexagonal network, honeycomb network, oxide network and silicate sheet network. Method: We use the technique of atom-bonds partition according to the valences of atoms to find results. Results: Exact values of valency-based molecular invariants, namely the Randić index, atom bond connectivity index, geometric arithmetic index, harmonic index, Zagreb indices, Zagreb polynomials, F-index and F-polynomial are found for four hexa chemical structures.

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