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.

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 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 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.

s-strongly perfect cartesian product of graphs

1992 ◽  
Vol 16 (4) ◽  
pp. 297-303
Author(s):  
Elefterie Olaru ◽  
Eugen M??ndrescu
Keyword(s):  
Cartesian Product ◽  
Cartesian Product Of Graphs ◽  
Product Of Graphs

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.

THE DIAMETER VARIABILITY OF THE CARTESIAN PRODUCT OF GRAPHS

2014 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
M. R. CHITHRA ◽  
A. VIJAYAKUMAR
Keyword(s):  
Interconnection Networks ◽  
Cartesian Product ◽  
Graph Products ◽  
Single Edge ◽  
Cartesian Product Of Graphs ◽  
Product Of Graphs

The diameter of a graph can be affected by the addition or deletion of edges. In this paper, we examine the Cartesian product of graphs whose diameter increases (decreases) by the deletion (addition) of a single edge. The problems of minimality and maximality of the Cartesian product of graphs with respect to its diameter are also solved. These problems are motivated by the fact that most of the interconnection networks are graph products and a good network must be hard to disrupt and the transmissions must remain connected even if some vertices or edges fail.

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
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.

scholarly journals On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 320 ◽  
Author(s):  
Young Kwun ◽  
Abaid Virk ◽  
Waqas Nazeer ◽  
M. Rehman ◽  
Shin Kang
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Molecular Compound ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Physico Chemical ◽  
Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

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