Testing the quality of molecular structure descriptors. Vertex-degree-based topological indices

The correlation ability of 20 vertex-degree-based topological indices, occurring in the chemical literature, is tested for the case of standard heats of formation and normal boiling points of octane isomers. It is found that the correlation ability of many of these indices is either rather weak or nil. The augmented Zagreb index and the atom-bond connectivity index yield the best results.

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Topological Indices of Certain Transformed Chemical Structures

Journal of Chemistry ◽

10.1155/2020/3045646 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xuewu Zuo ◽

Jia-Bao Liu ◽

Hifza Iqbal ◽

Kashif Ali ◽

Syed Tahir Raza Rizvi

Keyword(s):

Carbon Nanotube ◽

Line Graph ◽

Topological Indices ◽

Connectivity Index ◽

Zagreb Index ◽

Harmonic Index ◽

Chemical Structures ◽

Augmented Zagreb Index ◽

Carbon Nanotube Networks ◽

Atom Bond

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

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Zagreb Connection Indices of Two Dendrimer Nanostars

Acta Chemica Iasi ◽

10.2478/achi-2019-0001 ◽

2019 ◽

Vol 27 (1) ◽

pp. 1-14 ◽

Cited By ~ 6

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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On Topological Indices of Fractal and Cayley Tree Type Dendrimers

Discrete Dynamics in Nature and Society ◽

10.1155/2018/2684984 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Muhammad Imran ◽

Abdul Qudair Baig ◽

Waqas Khalid

Keyword(s):

Applied Sciences ◽

Cayley Tree ◽

Topological Indices ◽

Topological Descriptors ◽

Zagreb Index ◽

Physiochemical Properties ◽

Cayley Trees ◽

Augmented Zagreb Index ◽

Numerical Invariants ◽

Atom Bond

The topological descriptors are the numerical invariants associated with a chemical graph and are helpful in predicting their bioactivity and physiochemical properties. These descriptors are studied and used in mathematical chemistry, medicines, and drugs designs and in other areas of applied sciences. In this paper, we study the two chemical trees, namely, the fractal tree and Cayley tree. We also compute their topological indices based on degree concept. These indices include atom bond connectivity index, geometric arithmetic index and their fourth and fifth versions, Sanskruti index, augmented Zagreb index, first and second Zagreb indices, and general Randic index for α={-1,1,1/2,-1/2}. Furthermore, we give closed analytical results of these indices for fractal trees and Cayley trees.

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Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7

Advances in Materials Science and Engineering ◽

10.1155/2019/9594549 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12

Author(s):

Fei Deng ◽

Xiujun Zhang ◽

Mehdi Alaeiyan ◽

Abid Mehboob ◽

Mohammad Reza Farahani

Keyword(s):

Topological Indices ◽

Connectivity Index ◽

First Zagreb Index ◽

Zagreb Index ◽

Second Zagreb Index ◽

Randić Connectivity Index ◽

Augmented Zagreb Index ◽

Forgotten Index ◽

Atom Bond ◽

Modified Zagreb Index

In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometric-arithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.

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Degree-Based Topological Indices of Boron B12

Journal of Chemistry ◽

10.1155/2021/5563218 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Nouman Saeed ◽

Kai Long ◽

Zeeshan Saleem Mufti ◽

Hafsa Sajid ◽

Abdul Rehman

Keyword(s):

Chemical Structure ◽

Chemical Reactivity ◽

Molecular Descriptor ◽

Topological Indices ◽

Connectivity Index ◽

Melting Points ◽

Zagreb Index ◽

Boiling Points ◽

Electronic Parameters ◽

Atom Bond

Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as freezing points, boiling points, melting points, infrared spectrum, electronic parameters, viscosity, and density of chemical graphs. We discuss these topological indices, and some of them are mentioned here such as Randic index, the first general Zagreb index, the general sum connectivity index, hyper-Zagreb index (HM), the atom-bond connectivity index (ABC), the geometric-arithmetic index (GA), the harmonic index (H), and the forgotten index (F).

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Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

Journal of Chemistry ◽

10.1155/2021/7057412 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Muhammad Asad Ali ◽

Muhammad Shoaib Sardar ◽

Imran Siddique ◽

Dalal Alrowaili

Keyword(s):

Graph Theory ◽

Chemical Properties ◽

Topological Indices ◽

Connectivity Index ◽

Vaporization Enthalpy ◽

Zagreb Index ◽

Graph Operations ◽

Big Graphs ◽

Physical And Chemical ◽

Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1 and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

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On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

J ◽

10.3390/j2030026 ◽

2019 ◽

Vol 2 (3) ◽

pp. 384-409

Author(s):

Sourav Mondal ◽

Nilanjan De ◽

Anita Pal

Keyword(s):

Molecular Structure ◽

Network Theory ◽

Topological Index ◽

Applied Mathematics ◽

Reaction Network ◽

Topological Indices ◽

Zagreb Index ◽

Second Zagreb Index ◽

Real World Problems ◽

Chemical Reaction Network Theory

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

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Relating the ABC and harmonic indices

Journal of the Serbian Chemical Society ◽

10.2298/jsc130930001g ◽

2014 ◽

Vol 79 (5) ◽

pp. 557-563 ◽

Cited By ~ 4

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.

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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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Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph

Indonesian Journal of Combinatorics ◽

10.19184/ijc.2019.3.2.1 ◽

2020 ◽

Vol 3 (2) ◽

pp. 63

Author(s):

Salma Kanwal ◽

Mariam Imtiaz ◽

Ayesha Manzoor ◽

Nazeeran Idrees ◽

Ammara Afzal

Keyword(s):

Line Graph ◽

Topological Indices ◽

Point Graph ◽

Zagreb Index ◽

Harmonic Index ◽

Zagreb Indices ◽

Symmetric Division ◽

Augmented Zagreb Index ◽

Forgotten Index

Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, M-polynomials and some topological indices in term of the M-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.

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