Methods and algorithms for predicting the properties of chemical compounds by common fragments of molecular graphs

1998 ◽  
Vol 39 (1) ◽  
pp. 93-102 ◽  
Author(s):  
L. I. Makarov
Keyword(s):  
Chemical Compounds ◽  
Molecular Graphs

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 Characterization of (Molecular) Graphs with Fractional Metric Dimension as Unity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Javaid ◽  
Muhammad Kamran Aslam ◽  
Abdulaziz Mohammed Alanazi ◽  
Meshari M. Aljohani
Keyword(s):  
Ordered Set ◽  
Chemical Compounds ◽  
Diamond Lattice ◽  
Theoretical Development ◽  
Metric Dimension ◽  
Test Case ◽  
Molecular Graphs ◽  
Path Graph ◽  
Extremal Values

Distance-based dimensions provide the foreground for the identification of chemical compounds that are chemically and structurally different but show similarity in different reactions. The reason behind this similarity is the occurrence of a set S of atoms and their same relative distances to some ordered set T of atoms in both compounds. In this article, the aforementioned problem is considered as a test case for characterising the (molecular) graphs bearing the fractional metric dimension (FMD) as 1. For the illustration of the theoretical development, it is shown that the FMD of path graph is unity. Moreover, we evaluated the extremal values of fractional metric dimension of a tetrahedral diamond lattice.

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.

scholarly journals Some topological indices of dendrimers determined by their Banhatti polynomials

2020 ◽  
Vol 26 (1) ◽  
pp. 99-111
Author(s):  
Zheng-Qing Chu ◽  
Muhammad Salman ◽  
Asia Munir ◽  
Imran Khalid ◽  
Masood Ur Rehman ◽  
...  
Keyword(s):  
Molecular Structure ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Graphs

AbstractSeveral properties of chemical compounds in a molecular structure can be determined with the aid of mathematical languages provided by various types of topological indices. In this paper, we consider eight dendrimer structures in the context of valency based topological indices. We define four Banhatti polynomials for general (molecular) graphs, and compute them for underline dendrimers. We use these polynomials to determine four Banhatti indices. We also determine Zagreb (first, second and hyper) and forgotten indices by developing their relationships with Banhatti indices.

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.

scholarly journals The Topological Variable Computation for a Special Type of Cycloalkanes

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Wei Gao ◽  
Yaojun Chen ◽  
Weifan Wang
Keyword(s):  
Graph Theory ◽  
Chemical Compounds ◽  
Molecular Graphs ◽  
Distance Computation ◽  
Physical Chemical ◽  
Theoretical Tool

As an efficient theoretical tool, graph theory is widely used in computing chemistry. In terms of index computation on molecular graphs, the researchers can learn the potential properties of chemical compounds, including drugs, materials, and organics. In this paper, by means of distance computation, we study the eccentric version indices of cycloalkanes which occur quite frequently in the chemical drugs and other compounds. The promising prospects of the application for the physical, chemical, medical, and pharmacy engineering are illustrated by theoretical conclusions obtained in this article.

scholarly journals Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices of Generalized Bridge Molecular Graphs

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 751 ◽  
Author(s):  
Xiujun Zhang ◽  
Xinling Wu ◽  
Shehnaz Akhter ◽  
Muhammad Jamil ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Industry Research ◽  
Chemical Graph Theory ◽  
Chain Polymerization ◽  
Definition Of ◽  
Atom Bond

Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we propose a definition of generalized bridge molecular graphs that can model more kinds of long chain polymerization products than the bridge molecular graphs, and provide some results of the edge versions of atom-bond connectivity ( A B C e ) and geometric arithmetic ( G A e ) indices for some generalized bridge molecular graphs, which have regular, periodic and symmetrical structures. The results of this paper offer promising prospects in the applications for chemical and material engineering, especially in chemical industry research.

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.

scholarly journals Degree-based indices computation for special chemical molecular structures using edge dividing method

2016 ◽  
Vol 1 (1) ◽  
pp. 99-122 ◽  
Author(s):  
Wei Gao ◽  
Mohammad Reza Farahani
Keyword(s):  
Computational Chemistry ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Structures ◽  
Chemical Characteristics ◽  
Molecular Graphs

AbstractIn computational chemistry, the molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bound between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. In this paper, we report several degree based indices of some widely used chemical molecular structures by means of edge dividing technology.

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.

Sign in / Sign up

Export Citation Format

Share Document