scholarly journals Zagreb Connection Indices of Molecular Graphs Based on Operations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Jinde Cao ◽  
Usman Ali ◽  
Muhammad Javaid ◽  
Chuangxia Huang
Keyword(s):  
Chemical Compounds ◽  
Total Electron ◽  
Connection Number ◽  
Absolute Value ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Chemical Structures ◽  
Long Period ◽  
Linear Polynomial ◽  
Total Electron Energy

Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. The Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic Mol. Inform. 372018,1−7 restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.

Entire Zagreb indices of graphs

2018 ◽  
Vol 10 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Anwar Alwardi ◽  
Akram Alqesmah ◽  
R. Rangarajan ◽  
Ismail Naci Cangul
Keyword(s):  
Molecular Level ◽  
Chemical Compounds ◽  
Intermolecular Forces ◽  
Chemical Methods ◽  
Zagreb Indices ◽  
Molecular Graphs

The Zagreb indices have been introduced in 1972 to explain some properties of chemical compounds at molecular level mathematically. Since then, the Zagreb indices have been studied extensively due to their ease of calculation and their numerous applications in place of the existing chemical methods which needed more time and increased the costs. Many new kinds of Zagreb indices are recently introduced for several similar reasons. In this paper, we introduce the entire Zagreb indices by adding incidency of edges and vertices to the adjacency of the vertices. Our motivation in doing so was the following fact about molecular graphs: The intermolecular forces do not only exist between the atoms, but also between the atoms and bonds, so one should also take into account the relations (forces) between edges and vertices in addition to the relations between vertices to obtain better approximations to intermolecular forces. Exact values of these indices for some families of graphs are obtained and some important properties of the entire Zagreb indices are established.

scholarly journals Zagreb Connection Indices of Subdivision and Semi-Total Point Operations on Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Jiang-Hua Tang ◽  
Usman Ali ◽  
Muhammad Javaid ◽  
Khurram Shabbir
Keyword(s):  
Cartesian Product ◽  
Vital Role ◽  
Acentric Factor ◽  
Total Electron ◽  
Molecular Graphs ◽  
Total Electron Energy ◽  
Long Time ◽  
Total Point ◽  
Physicochemical And Structural Properties ◽  
First Time

Representation or coding of the molecular graphs with the help of numerical numbers plays a vital role in the studies of physicochemical and structural properties of the chemical compounds that are involved in the molecular graphs. For the first time, the modified first Zagreb connection index appeared in the paper by Gutman and Trinajstic (1972) to compute total electron energy of the alternant hydrocarbons, but after that, for a long time, it has not been studied. Recently, Ali and Trinajstic (2018) restudied the first Zagreb connection index ZC1, the second Zagreb connection index ZC2, and the modified first Zagreb connection index ZC1∗ to find entropy and acentric factor of the octane isomers. They also reported that the values provided by the International Academy of Mathematical Chemistry show better chemical capability of the Zagreb connection indices than the ordinary Zagreb indices. Assume that S1 and S2 denote the operations of subdivision and semitotal point, respectively. Then, the S-sum graphs Q1+QS2 are obtained by the cartesian product of SQ1 and Q2, where S∈S1,S2, Q1andQ2 are any connected graphs, and SQ1 is a graph obtained after applying the operation S on Q1. In this paper, we compute the Zagreb connection indices (ZC1, ZC2, and ZC1∗) of the S-sum graphs in terms of various topological indices of their factor graphs. At the end, as an application of the computed results, the Zagreb connection indices of the S-sum graphs obtained by the particular classes of alkanes are also included.

scholarly journals Estimating the total π-electron energy

2013 ◽  
Vol 78 (12) ◽  
pp. 1925-1933 ◽  
Author(s):  
Ivan Gutman ◽  
Kinkar Das
Keyword(s):  
Electron Energy ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Total Electron ◽  
Molecular Graphs ◽  
Conjugated Hydrocarbons ◽  
Short Survey ◽  
Total Electron Energy ◽  
Graph Energy

The paper gives a short survey of the most important lower and upper bounds for total ?-electron energy, i.e., graph energy (E). In addition, a new lower and a new upper bound for E are deduced, valid for general molecular graphs. The strengthened versions of these estimates, valid for alternant conjugated hydrocarbons, are also reported.

scholarly journals Modified Zagreb connection indices of the T-sum graphs

2020 ◽  
Vol 43 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Usman Ali ◽  
Muhammad Javaid ◽  
Agha Kashif
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Line Graphs ◽  
Real Numbers ◽  
Statistical Tools ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Octane Isomers

AbstractThe quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

Some valency oriented molecular invariants of certain networks.

2020 ◽  
Vol 23 ◽  
Author(s):  
Muhammad Salman ◽  
Faisal Ali ◽  
Masood Ur Rehman ◽  
Imran Khalid
Keyword(s):  
Molecular Structure ◽  
Boiling Point ◽  
Strain Energy ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
Atom Bond ◽  
Honeycomb Network ◽  
Silicate Sheet

Background: The valency of an atom in a molecular structure is the number of its neighboring atoms. A large number of valency based molecular invariants have been conceived, which correlate certain physio-chemical properties like boiling point, stability, strain energy and many more of chemical compounds. Objective: Our aim is to study the valency based molecular invariants for four hexa chemical structures, namely hexagonal network, honeycomb network, oxide network and silicate sheet network. Method: We use the technique of atom-bonds partition according to the valences of atoms to find results. Results: Exact values of valency-based molecular invariants, namely the Randić index, atom bond connectivity index, geometric arithmetic index, harmonic index, Zagreb indices, Zagreb polynomials, F-index and F-polynomial are found for four hexa chemical structures.

scholarly journals Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1320
Author(s):  
Usman Ali ◽  
Muhammad Javaid ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Carbon Nanotube ◽  
Electron Energy ◽  
Upper Bounds ◽  
Molecular Networks ◽  
Connection Number ◽  
Zagreb Indices ◽  
Linear Polynomial ◽  
Degree Of A Vertex ◽  
Octane Isomers ◽  
Alternant Hydrocarbons

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks.

scholarly journals Zagreb Polynomials and Redefined Zagreb Indices for Chemical Structures Helpful in the Treatment of COVID-19

2020 ◽  
Vol 4 (4) ◽  
pp. 33-40
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index (TI) is a number that is helpful in predicting the properties of chemical compounds. We can estimate the physical and chemical properties of several chemical compounds. In this study, we compute Zagreb polynomials and the redefined Zagreb indices for chemical compounds used in the treatment of COVID-19 namely remdesivir, chloroquine, hydroxychloroquine and theaflavin.

scholarly journals Total π-electron energy and Laplacian energy: How far the analogy goes?

2007 ◽  
Vol 72 (12) ◽  
pp. 1343-1350 ◽  
Author(s):  
Slavko Radenkovic ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Molecular Graph ◽  
Total Electron ◽  
Good Linear ◽  
Molecular Graphs ◽  
Acyclic Graphs ◽  
Laplacian Energy ◽  
Total Electron Energy ◽  
Good Linear Correlation

The Laplacian energy LE is a newly introduced molecular-graph-based analog of the total ?-electron energy E. It is shown that LE and E have a similar structure-dependency only when molecules of different sizes are compared, when a good linear correlation between them exists. Within classes of isomers, LE and E are either not correlated at all or (as in the case of acyclic systems) are inversely proportional. The acyclic graphs and molecular graphs having the greatest and smallest LE values (determined in this work) differ significantly from those (previously known) having the greatest and smallest E values.

scholarly journals Computing entire Zagreb indices of some dendrimer structures

2020 ◽  
Vol 43 (1) ◽  
pp. 229-236
Author(s):  
Wei Gao ◽  
Zahid Iqbal ◽  
Abdul Jaleel ◽  
Adnan Aslam ◽  
Muhammad Ishaq ◽  
...  
Keyword(s):  
Molecular Level ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Chemical Methods ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Qspr Study

AbstractTopological indices are numerical numbers associated to molecular graphs and are invariant of a graph. In QSAR/QSPR study, Zagreb indices are used to explain the different properties of chemical compounds at the molecular level mathematically. They have been studied extensively due to their ease of calculation and numerous applications in place of the existing chemical methods which needed more time and increased the costs. In this paper, we compute precise values of new versions of Zagreb indices for two classes of dendrimers.

Therapeutic Properties of Several Chemical Compounds from Salvia officinalis L. in Alzheimer’s Disease

2020 ◽  
Vol 21 ◽  
Author(s):  
Georgiana Uță ◽  
Denisa Ștefania Manolescu ◽  
Speranța Avram
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Side Effects ◽  
Chemical Compounds ◽  
Natural Compounds ◽  
Salvia Officinalis ◽  
Chemical Structures ◽  
In Silico Studies ◽  
Wide Range ◽  
Salvia Officinalis L

Background.: Currently, the pharmacological management in Alzheimer's disease is based on several chemical structures, represented by acetylcholinesterase and N-methyl-D-aspartate (NMDA) receptor ligands, with still unclear molecular mechanisms, but severe side effects. For this reason, a challenge for Alzheimer's disease treatment remains to identify new drugs with reduced side effects. Recently, the natural compounds, in particular certain chemical compounds identified in the essential oil of peppermint, sage, grapes, sea buckthorn, have increased interest as possible therapeutics. Objectives.: In this paper, we have summarized data from the recent literature, on several chemical compounds extracted from Salvia officinalis L., with therapeutic potential in Alzheimer's disease. Methods.: In addition to the wide range of experimental methods performed in vivo and in vitro, also we presented some in silico studies of medicinal compounds. Results. Through this mini-review, we present the latest information regarding the therapeutic characteristics of natural compounds isolated from Salvia officinalis L. in Alzheimer's disease. Conclusion.: Thus, based on the information presented, we can say that phytotherapy is a reliable therapeutic method in a neurodegenerative disease.

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