scholarly journals Irregularity Measures for Metal-Organic Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Xuan Guo ◽  
Yu-Ming Chu ◽  
Muhammad Khalid Hashmi ◽  
Abaid Ur Rehman Virk ◽  
Jingjng Li
Keyword(s):  
Molecular Structure ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Metal Organic ◽  
Single Number ◽  
Organic Networks

Topological index plays an important role in predicting physicochemical properties of a molecular structure. With the help of the topological index, we can associate a single number with a molecular graph. Drugs and other chemical compounds are frequently demonstrated as different polygonal shapes, trees, graphs, etc. In this paper, we will compute irregularity indices for metal-organic networks.

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.

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.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

On topological indices of poly oxide, poly silicate, DOX, and DSL networks

2015 ◽  
Vol 93 (7) ◽  
pp. 730-739 ◽  
Author(s):  
Abdul Qudair Baig ◽  
Muhammad Imran ◽  
Haidar Ali
Keyword(s):  
Molecular Structure ◽  
Graph Theory ◽  
Physicochemical Properties ◽  
Interconnection Networks ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Silicate Network ◽  
Graph Invariant ◽  
Qspr Study ◽  
Atom Bond

Topological indices 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 (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study different interconnection networks and derive analytical closed results of the general Randić index (Rα(G)) for α = 1, [Formula: see text], –1, [Formula: see text] only, for dominating oxide network (DOX), dominating silicate network (DSL), and regular triangulene oxide network (RTOX). All of the studied interconnection networks in this paper are motivated by the molecular structure of a chemical compound, SiO4. We also compute the general first Zagreb, ABC, GA, ABC4, and GA5 indices and give closed formulae of these indices for these interconnection networks.

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.

Computing Analysis of Degree and Connection Based Irregular Indices of Polycyclic Aromatic Hydrocarbons

2021 ◽  
Vol 18 ◽  
Author(s):  
Muhammad Javaid ◽  
Muhammad Ibraheem ◽  
Abdul Raheem
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Medical Science ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Molecular Graphs ◽  
Equal Degree ◽  
Physical Chemical ◽  
Polycyclic Aromatic

Introduction: A graph is supposed to be regular if all vertices have equal degree, otherwise irregular. Materials and Methods: Polycyclic aromatic hydrocarbons are important combusting material and considered as class of carcinogens. These polycyclic aromatic hydrocarbons play an important role in graphitisation of medical science. A topological index is a function that assigns a numerical value to a (molecular) graph which predicts various physical, chemical, biological, thermodynamical and structural properties of (molecular) graphs. An irregular index is a topological index that measures the irregularity of atoms with respect to their bonding for the chemical compounds which are involved in the under studying graphs. Results and Discussion: In this paper, we will compute an analysis of distance based irregular indices of polycyclic aromatic hydrocarbons. A comparison among the obtained indices with the help of their numerical values and the 3D presentations is also included. The efficient and steady indices of polycyclic aromatic hydrocarbons are addressed in the form of their irregularities. Conclusion: Connection based study of the molecular graphs is more suitable than the degree based irregularity indices.

Computing and Analysis of Topological Co-Indices for Metal-Organic Compound

2021 ◽  
Vol 18 ◽  
Author(s):  
Dongming Zhao ◽  
Mehwish Hussain Muhammad ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Nasir ◽  
Muhammad Faisal Nadeem ◽  
...  
Keyword(s):  
Molecular Structure ◽  
Organic Compound ◽  
Physicochemical Properties ◽  
Quantitative Structure ◽  
Atomic Structures ◽  
Topological Descriptor ◽  
Vertex Set ◽  
Metal Organic

: A topological descriptor is a mathematical illustration of a molecular construction that relates particular physicochemical properties of primary molecular structure as well its mathematical depiction. Topological co-indices are usually applied for quantitative structure actions relationships (QSAR) and quantitative structures property relationships (QSPR). Topological co-indices are topological descriptor which considered the noncontiguous vertex set. At this point, we study the accompanying some renowned topological co-indices: the 1st and 2nd Zagreb co-indices, the 1st and 2nd multiplicative Zagreb co-indices and the F-coindex. By applying structure basics examinations and deductions, we discuss the earlier stated co-indices of few synthetic atomic structures that frequently comes in clinical, synthetic, and material designing.

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 Zagreb Connection Indices of Two Dendrimer Nanostars

2019 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Nisar Fatima ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Physicochemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Octane Isomers ◽  
The First Zagreb Index

Abstract It is well known fact that several physicochemical properties of chemical compounds are closely related to their molecular structure. Mathematical chemistry provides a method to predict the aforementioned properties of compounds using topological indices. The Zagreb indices are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [Ali, A.; Trinajstić, N. A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO] 2017; Mol. Inform. 2018, 37, 1800008] and [Naji, A. M.; Soner, N. D.; Gutman, I. On leap Zagreb indices of graphs, Commun. Comb. Optim. 2017, 2, 99–117], which were named as the Zagreb connection indices and the leap Zagreb indices, respectively. In this paper, we check the chemical applicability of the newly considered Zagreb connection indices on the set of octane isomers and establish general expressions for calculating these indices of two well-known dendrimer nanostars.

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