Multiplicative Degree Based Topological Indices of Nanostar Dendrimers

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.

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Computations of the M-Polynomials and Degree-Based Topological Indices for Dendrimers and Polyomino Chains

International Journal of Analytical Chemistry ◽

10.1155/2018/1709073 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Young Chel Kwun ◽

Adeel Farooq ◽

Waqas Nazeer ◽

Zohaib Zahid ◽

Saba Noreen ◽

...

Keyword(s):

Physicochemical Properties ◽

Boiling Point ◽

Strain Energy ◽

Chemical Compounds ◽

Pamam Dendrimers ◽

Topological Indices

Topological indices correlate certain physicochemical properties like boiling point, stability, and strain energy of chemical compounds. In this report, we compute M-polynomials for PAMAM dendrimers and polyomino chains. Moreover, by applying calculus, we compute nine important topological indices of under-study dendrimers and chains.

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Degree-based topological indices of double graphs and strong double graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830917500665 ◽

2017 ◽

Vol 09 (05) ◽

pp. 1750066 ◽

Cited By ~ 7

Author(s):

Muhammad Imran ◽

Shehnaz Akhter

Keyword(s):

Graph Theory ◽

Physicochemical Properties ◽

Boiling Point ◽

Strain Energy ◽

Chemical Compounds ◽

Topological Indices ◽

First Zagreb Index ◽

Original Graph ◽

Zagreb Index ◽

Zagreb Indices

The topological indices are useful tools to the theoretical chemists that are provided by the graph theory. They correlate certain physicochemical properties such as boiling point, strain energy, stability, etc. of chemical compounds. For a graph [Formula: see text], the double graph [Formula: see text] is a graph obtained by taking two copies of graph [Formula: see text] and joining each vertex in one copy with the neighbors of corresponding vertex in another copy and strong double graph SD[Formula: see text] of the graph [Formula: see text] is the graph obtained by taking two copies of the graph [Formula: see text] and joining each vertex [Formula: see text] in one copy with the closed neighborhood of the corresponding vertex in another copy. In this paper, we compute the general sum-connectivity index, general Randi[Formula: see text] index, geometric–arithmetic index, general first Zagreb index, first and second multiplicative Zagreb indices for double graphs and strong double graphs and derive the exact expressions for these degree-base topological indices for double graphs and strong double graphs in terms of corresponding index of original graph [Formula: see text].

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Irregularity Measures for Benzene Ring Embedded in P-Type Surface

Mathematical Problems in Engineering ◽

10.1155/2020/2462530 ◽

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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Computation of Zagreb and atom-bond connectivity indices of certain families of dendrimers by using automorphism group action

Journal of the Serbian Chemical Society ◽

10.2298/jsc160718096a ◽

2017 ◽

Vol 82 (2) ◽

pp. 151-162

Author(s):

Uzma Ahmad ◽

Sarfraz Ahmad ◽

Rabia Yousaf

Keyword(s):

Automorphism Group ◽

Carbon Atom ◽

Physicochemical Properties ◽

Group Action ◽

Chemical Compounds ◽

Topological Indices ◽

Zagreb Indices ◽

Connectivity Indices ◽

Atom Bond

In QSAR/QSPR studies, topological indices are utilized to predict the bioactivity of chemical compounds. In this paper, the closed forms of different Zagreb indices and atom?bond connectivity indices of regular dendrimers G[n] and H[n] in terms of a given parameter n are determined by using the automorphism group action. It was reported that these connectivity indices are correlated with some physicochemical properties and are used to measure the level of branching of the molecular carbon-atom skeleton.

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On the Wiener index and variants of the Szeged index of single-walled titania nanotubes TiO2(m,n)

Canadian Journal of Chemistry ◽

10.1139/cjc-2016-0458 ◽

2017 ◽

Vol 95 (1) ◽

pp. 68-86 ◽

Cited By ~ 1

Author(s):

Muhammad Imran ◽

Sabeel-e Hafi

Keyword(s):

Physicochemical Properties ◽

Strain Energy ◽

Chemical Compounds ◽

Wiener Index ◽

Exact Expression ◽

Topological Indices ◽

Titania Nanotubes ◽

Graph Invariant ◽

Szeged Index ◽

Cut Method

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. There are certain types of topological indices such as degree-based topological indices, distance-based topological indices, and counting-related topological indices. These topological indices correlate certain physicochemical properties such as boiling point, stability, and strain energy of chemical compounds. In this paper, we compute an exact expression of Wiener index, vertex-Szeged index, edge-Szeged index, and total-Szeged index of single-walled titania nanotubes TiO2(m, n) by using the cut method for all values of m and n.

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On degree-based topological descriptors of strong product graphs

Canadian Journal of Chemistry ◽

10.1139/cjc-2015-0562 ◽

2016 ◽

Vol 94 (6) ◽

pp. 559-565 ◽

Cited By ~ 3

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.

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

Canadian Journal of Chemistry ◽

10.1139/cjc-2014-0490 ◽

2015 ◽

Vol 93 (7) ◽

pp. 730-739 ◽

Cited By ~ 36

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.

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

Mathematical Problems in Engineering ◽

10.1155/2021/6019517 ◽

2021 ◽

Vol 2021 ◽

pp. 1-19 ◽

Cited By ~ 1

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.

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On molecular topological properties of dendrimers

Canadian Journal of Chemistry ◽

10.1139/cjc-2015-0466 ◽

2016 ◽

Vol 94 (2) ◽

pp. 120-125 ◽

Cited By ~ 7

Author(s):

Syed Ahtsham Ul Haq Bokhary ◽

Muhammad Imran ◽

Sadia Manzoor

Keyword(s):

Graph Theory ◽

Physicochemical Properties ◽

Chemical Compounds ◽

Topological Indices ◽

Topological Properties ◽

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 the Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of different chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study the degree-based molecular topological indices such as ABC4 and GA5 for certain families of dendrimers. We derive the analytical closed formulae for these classes of dendrimers.

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