Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. Topological indices help us collect information about algebraic graphs and give us mathematical approach to understand the properties of algebraic structures. With the help of topological indices, we can guess the properties of chemical compounds without performing experiments in wet lab. There are more than 148 topological indices in the literature, but none of them completely give all properties of under study compounds. Together, they do it to some extent; hence, there is always room to introduce new indices. In this paper, we present first and second reserve Zagreb indices and first reverse hyper-Zagreb indices, reverse GA index, and reverse atomic bond connectivity index for the crystallographic structure of molecules. We also present first and second reverse Zagreb polynomials and first and second reverse hyper-Zagreb polynomials for the crystallographic structure of molecules.

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On Molecular Topological Properties of TiO2 Nanotubes

Journal of Nanoscience ◽

10.1155/2016/1028031 ◽

2016 ◽

Vol 2016 ◽

pp. 1-5 ◽

Cited By ~ 3

Author(s):

Nilanjan De

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Strong Correlation ◽

Tio2 Nanotubes ◽

Chemical Compounds ◽

Topological Indices ◽

Topological Properties ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Titania Nanotube

Titania nanotube is a well-known semiconductor and has numerous technological applications. In chemical graph theory, topological indices provide an important tool to quantify the molecular structure and it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Among different topological indices, degree-based topological indices are most studied and have some important applications. In this study, several old and new degree-based topological indices have been investigated for titania TiO2 nanotubes.

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On Realization and Characterization of Topological Indices

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.a4135.119119 ◽

2019 ◽

Vol 9 (1) ◽

pp. 715-718

Keyword(s):

Topological Index ◽

Fixed Number ◽

Topological Indices ◽

Molecular Structures ◽

Real Numbers ◽

Graph Invariants ◽

Chemical Graph ◽

Zagreb Indices ◽

Chemical Graph Theory

In chemical graph theory, topological index is one of the graph invariants which is a fixed number based on structure of a graph. Topological index is used as one of the tool to analyze molecular structures and for proper and optimal design of nanostructure. In this paper we realize the real numbers that are topological indices such as Zagreb indices, Randic index, NK-index, multiplicative F-index and multiplicative Zagreb indices along with some characterizations.

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Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn

Journal of Chemistry ◽

10.1155/2019/4291943 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

Hai-Xia Li ◽

Sarfaraz Ahmad ◽

Iftikhar Ahmad

Keyword(s):

Topological Index ◽

Molecular Descriptor ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Chemical Graph ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Chemical Graph Theory ◽

Augmented Zagreb Index

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In this paper, M-polynomial OKn and OPn networks are computed. The M-polynomial is rich in information about degree-based topological indices. By applying the basic rules of calculus on M-polynomials, the first and second Zagreb indices, modified second Zagreb index, general Randić index, inverse Randić index, symmetric division index, harmonic index, inverse sum index, and augmented Zagreb index are recovered.

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Computing SS Index of Certain Dendrimers

Journal of Mathematics ◽

10.1155/2021/7483508 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Weidong Zhao ◽

M.C. Shanmukha ◽

A. Usha ◽

Mohammad Reza Farahani ◽

K.C. Shilpa

Keyword(s):

Chemical Structure ◽

Topological Index ◽

Chemical Compounds ◽

Biological Properties ◽

Molar Refraction ◽

Topological Indices ◽

Zagreb Indices ◽

Mathematical Properties ◽

Chemical Graph Theory ◽

Physico Chemical

The numerical descriptor gathers the data from the molecular graphs and helps to know the characteristics of the chemical structure known as topological index. The QSAR/QSPR/QSTR studies are benefited with the significant role played by topological indices in the drug design. Topological indices provide the information about the physical/chemical/biological properties of chemical compounds. The Zagreb indices are widely studied because of their extensive usage in chemical graph theory. Inspired by the earlier work on inverse sum indeg index (ISI index), novel topological index known as SS index is introduced and computed for four dendrimer structures. Also, the strong correlation coefficient between SS index and 5 physico-chemical characteristics such as boiling point (bp), molar volume (mv), molar refraction (mr), heats of vaporization (hv), and critical pressure (cp) of 67 alkane isomers have been determined. It is found that newly introduced index has shown good correlation in comparison with three most popular existing indices (ISI index and first and second Zagreb indices). In the last part, the mathematical properties of SS index are discussed.

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Tetracyclic graphs with maximum second Zagreb index: A simple approach

Asian-European Journal of Mathematics ◽

10.1142/s179355711850064x ◽

2018 ◽

Vol 11 (05) ◽

pp. 1850064 ◽

Cited By ~ 5

Author(s):

Akbar Ali

Keyword(s):

Graph Theory ◽

Short Note ◽

Topological Indices ◽

Simple Approach ◽

Graph Invariants ◽

Zagreb Index ◽

Chemical Graph ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Chemical Graph Theory

In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum [Formula: see text] value among all members of the collection [Formula: see text]. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.

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On ve-degree- and ev-degree-based topological properties of crystallographic structure of cuprite Cu2O

Open Chemistry ◽

10.1515/chem-2021-0051 ◽

2021 ◽

Vol 19 (1) ◽

pp. 576-585

Author(s):

Shu-Bo Chen ◽

Abdul Rauf ◽

Muhammad Ishtiaq ◽

Muhammad Naeem ◽

Adnan Aslam

Keyword(s):

Graph Theory ◽

Copper Oxide ◽

Topological Indices ◽

Topological Descriptors ◽

Crystallographic Structure ◽

Chemical Substances ◽

Chemical Graph ◽

Chemical Structures ◽

Chemical Graph Theory ◽

Enormous Number

Abstract In the study of chemical graph theory, an enormous number of research analyses have confirmed that the characteristics of chemicals have a nearby connection with their atomic structure. Topological indices were the critical tools for the analysis of these chemical substances to consider the essential topology of chemical structures. Topological descriptors are the significant numerical quantities or invariant in the fields of chemical graph theory. In this study, we have studied the crystal structure of copper oxide ( Cu 2 O {{\rm{Cu}}}_{2}{\rm{O}} ) chemical graph, and further, we have calculated the ev-degree- and ve-degree-based topological indices of copper oxide chemical graph. This kind of study may be useful for understanding the atomic mechanisms of corrosion and stress–corrosion cracking of copper.

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On Degree-Based Topological Indices of Symmetric Chemical Structures

Symmetry ◽

10.3390/sym10110619 ◽

2018 ◽

Vol 10 (11) ◽

pp. 619 ◽

Cited By ~ 2

Author(s):

Jia-Bao Liu ◽

Haidar Ali ◽

Muhammad Shafiq ◽

Usman Munir

Keyword(s):

Molecular Descriptor ◽

Molecular Graph ◽

Chemical Properties ◽

Chemical Compounds ◽

Topological Indices ◽

Chemical Structures ◽

Physico Chemical ◽

First Time ◽

Ga Index ◽

Atom Bond

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index 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 HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randić index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

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M-polynomial and topological indices of zigzag edge coronoid fused by starphene

Open Chemistry ◽

10.1515/chem-2020-0161 ◽

2020 ◽

Vol 18 (1) ◽

pp. 1362-1369

Author(s):

Farkhanda Afzal ◽

Sabir Hussain ◽

Deeba Afzal ◽

Saira Hameed

Keyword(s):

Graph Theory ◽

Chemical Properties ◽

Topological Indices ◽

Zigzag Edge ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Chemical Graphs

AbstractChemical graph theory is a subfield of graph theory that studies the topological indices for chemical graphs that have a good correlation with chemical properties of a chemical molecule. In this study, we have computed M-polynomial of zigzag edge coronoid fused by starphene. We also investigate various topological indices related to this graph by using their M-polynomial.

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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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Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)

Discrete Dynamics in Nature and Society ◽

10.1155/2019/8696982 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Lian Chen ◽

Abid Mehboob ◽

Haseeb Ahmad ◽

Waqas Nazeer ◽

Muhammad Hussain ◽

...

Keyword(s):

Topological Index ◽

Molecular Descriptor ◽

Wiener Index ◽

Vital Role ◽

Harary Index ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Hosoya Polynomial ◽

Molecular Branching ◽

Path Number

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we computed the Hosoya and the Harary polynomials for TOX(n),RTOX(n),TSL(n), and RTSL(n) networks. Moreover, we computed serval distance based topological indices, for example, Wiener index, Harary index, and multiplicative version of wiener index.

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