scholarly journals Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-19 ◽  
Author(s):  
Muhammad Javaid ◽  
Usman Ali ◽  
Jia-Bao Liu
Keyword(s):  
Tensor Product ◽  
Physicochemical Properties ◽  
Electron Energy ◽  
Topological Index ◽  
Chemical Compounds ◽  
Upper Bounds ◽  
Symmetric Difference ◽  
Factor Graphs ◽  
Strong Product ◽  
Alternant Hydrocarbons

A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali and Trinajstić studied the first Zagreb connection index Z C 1 to evaluate the value of a molecule. This concept was first studied by Gutman and Trinajstić in 1972 to find the solution of π -electron energy of alternant hydrocarbons. In this paper, the first Zagreb connection index and coindex are obtained in the form of exact formulae and upper bounds for the resultant graphs in terms of different indices of their factor graphs, where the resultant graphs are obtained by the product-related operations on graphs such as tensor product, strong product, symmetric difference, and disjunction. At the end, an analysis of the obtained results for the first Zagreb connection index and coindex on the aforesaid resultant graphs is interpreted with the help of numerical values and graphical depictions.

scholarly journals A Computational Approach on Acetaminophen Drug using Degree-Based Topological Indices and M-Polynomials

2021 ◽  
Vol 12 (6) ◽  
pp. 7249-7266
Keyword(s):  
Biological Activity ◽  
Physicochemical Properties ◽  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Chemical Compounds ◽  
Computational Approach ◽  
Topological Indices ◽  
Numerical Representation ◽  
Essential Drug

Topological index is a numerical representation of a chemical structure. Based on these indices, physicochemical properties, thermodynamic behavior, chemical reactivity, and biological activity of chemical compounds are calculated. Acetaminophen is an essential drug to prevent/treat various types of viral fever, including malaria, flu, dengue, SARS, and even COVID-19. This paper computes the sum and multiplicative version of various topological indices such as General Zagreb, General Randić, General OGA, AG, ISI, SDD, Forgotten indices M-polynomials of Acetaminophen. To the best of our knowledge, for the Acetaminophen drugs, these indices have not been computed previously.

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 On the Exact Values of HZ-Index for the Graphs under Operations

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Dalal Awadh Alrowaili ◽  
Saira Javed ◽  
Muhammad Javaid
Keyword(s):  
Real Number ◽  
Topological Index ◽  
Factor Graphs ◽  
Real Numbers ◽  
Zagreb Indices ◽  
Strong Product

Topological index (TI) is a function from the set of graphs to the set of real numbers that associates a unique real number to each graph, and two graphs necessarily have the same value of the TI if these are structurally isomorphic. In this note, we compute the HZ − index of the four generalized sum graphs in the form of the various Zagreb indices of their factor graphs. These graphs are obtained by the strong product of the graphs G and D k G , where D k ∈ S k , R k , Q k , T k represents the four generalized subdivision-related operations for the integral value of k ≥ 1 and D k G is a graph that is obtained by applying D k on G . At the end, as an illustration, we compute the HZ − index of the generalized sum graphs for exactly k = 1 and compare the obtained results.

scholarly journals The Second Hyper-Zagreb Coindex of Chemical Graphs and Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ahmed Ayache ◽  
Abdu Alameri ◽  
Mohammed Alsharafi ◽  
Hanan Ahmed
Keyword(s):  
Tensor Product ◽  
Topological Index ◽  
Molecular Graph ◽  
Cartesian Product ◽  
Explicit Formulas ◽  
Chemical Graph ◽  
Strong Product ◽  
Chemical Graphs ◽  
Product Composition ◽  
Graph Structures

The second hyper-Zagreb coindex is an efficient topological index that enables us to describe a molecule from its molecular graph. In this current study, we shall evaluate the second hyper-Zagreb coindex of some chemical graphs. In this study, we compute the value of the second hyper-Zagreb coindex of some chemical graph structures such as sildenafil, aspirin, and nicotine. We also present explicit formulas of the second hyper-Zagreb coindex of any graph that results from some interesting graphical operations such as tensor product, Cartesian product, composition, and strong product, and apply them on a q-multiwalled nanotorus.

Product version of reciprocal Gutman indices of composite graphs

2017 ◽  
Vol 26 (2) ◽  
pp. 211-219
Author(s):  
K. Pattabiraman
Keyword(s):  
Tensor Product ◽  
Upper Bounds ◽  
Graph Invariants ◽  
Harary Index ◽  
Connected Graphs ◽  
Zagreb Indices ◽  
Strong Product

In this paper, we present the upper bounds for the product version of reciprocal Gutman indices of the tensor product, join and strong product of two connected graphs in terms of other graph invariants including the Harary index and Zagreb indices.

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 Multiplicative Degree Based Topological Indices of Nanostar Dendrimers

2020 ◽  
Vol 11 (1) ◽  
pp. 7700-7711 ◽  
Keyword(s):  
Physicochemical Properties ◽  
Building Block ◽  
Boiling Point ◽  
Topological Index ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Pharmaceutical Sciences ◽  
Molecular Topology ◽  
Acentric Factor ◽  
Branched Nanostructures

A topological index is a numerical quantity connected with a graph describing the molecular topology of the graph. It can predict different physicochemical properties such as boiling point, entropy, acentric factor etc. of chemical compounds. Dendrimers are highly branched nanostructures that are regarded as a building block in nanotechnology having wide applications. In this paper, multiplicative degree-based topological indices are computed for some nanostar dendrimers. The derived results have the potential for implementation in the chemical, biological, and pharmaceutical sciences.

scholarly journals Sharp Bounds for the Inverse Sum Indeg Index of Graph Operations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Anam Rani ◽  
Muhammad Imran ◽  
Usman Ali
Keyword(s):  
Tensor Product ◽  
Physicochemical Properties ◽  
Cartesian Product ◽  
Total Surface Area ◽  
Sharp Bounds ◽  
Graph Operations ◽  
Strong Product ◽  
Octane Isomers ◽  
International Academy ◽  
Corona Product

Vukičević and Gasperov introduced the concept of 148 discrete Adriatic indices in 2010. These indices showed good predictive properties against the testing sets of the International Academy of Mathematical Chemistry. Among these indices, twenty indices were taken as beneficial predictors of physicochemical properties. The inverse sum indeg index denoted by ISI G k of G k is a notable predictor of total surface area for octane isomers and is presented as ISI G k = ∑ g k g k ′ ∈ E G k d G k g k d G k g k ′ / d G k g k + d G k g k ′ , where d G k g k represents the degree of g k ∈ V G k . In this paper, we determine sharp bounds for ISI index of graph operations, including the Cartesian product, tensor product, strong product, composition, disjunction, symmetric difference, corona product, Indu–Bala product, union of graphs, double graph, and strong double graph.

scholarly journals Irregularity Measures for Benzene Ring Embedded in P-Type Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yun Liu ◽  
Aysha Siddiqa ◽  
Yu-Ming Chu ◽  
Muhammad Azam ◽  
Muhammad Asim Raza Basra ◽  
...  
Keyword(s):  
Physicochemical Properties ◽  
Benzene Ring ◽  
Chemical Compound ◽  
Topological Index ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Single Number ◽  
P Type

A topological index is an important tool in predicting physicochemical properties of a chemical compound. Topological indices help us to assign a single number to a chemical compound. Drugs and other chemical compounds are frequently demonstrated as different polygonal shapes, trees, graphs, etc. In this paper, we will compute irregularity indices for the benzene ring embedded in a P-type surface BRp and the simple bounded dual of the benzene ring embedded in a P-type surface SBRp.

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