Computing topological polynomials of mesh-derived networks

2018 ◽  
Vol 10 (06) ◽  
pp. 1850077 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Qudair Baig ◽  
Shafiq Ur Rehman ◽  
Haidar Ali ◽  
Roslan Hasni
Keyword(s):  
Mesh Networks ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Descriptors ◽  
Cut Edge ◽  
Physico Chemical ◽  
First Time ◽  
Ga Index ◽  
Atom Bond

Topological descriptors are numerical parameters of a molecular graph which characterize its molecular topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity [Formula: see text] 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. The counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. All of the studied interconnection mesh networks in this paper are motivated by the molecular structure of a Sodium chloride NaCl. In this paper, Omega, Sadhana and PI polynomials are computed for mesh-derived networks. These polynomials were proposed on the ground of quasi-orthogonal cut edge strips in polycyclic graphs. These polynomials count equidistant and non-equidistant edges in graphs. Moreover, the analytical closed formulas of these polynomials for mesh-derived networks are computed for the first time.

scholarly journals On Degree-Based Topological Indices of Symmetric Chemical Structures

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 619 ◽  
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.

scholarly journals A new approach in topological descriptors usage. Iterated line graphs in the theoretical prediction of physico-chemical properties of saturated hydrocarbons

2019 ◽  
Keyword(s):  
Boiling Point ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Descriptors ◽  
Vaporization Enthalpy ◽  
Line Graphs ◽  
Regression Equations ◽  
Saturated Hydrocarbons ◽  
Program Complex ◽  
Physico Chemical

A new look on the problem of the molecular systems index description is presented. The capabilities of iterated line (edge) graphs in characterization of saturated hydrocarbons properties were investigated. It was demonstrated that single selected molecular (graph-theoretical (topological) or informational) descriptor calculated for the sequence of nested line graphs provides quite reliable progressive set of regression equations. Hence, the problem of descriptor set reduction is solved in the presented approach at list partially. Corresponding program complex (QUASAR) has been implemented with Python 3 program language. As the test example physico-chemical properties of octane isomers have been chosen. Among the properties under investigation there are boiling point, critical temperature, critical pressure, enthalpy of vaporization, enthalpy of formation, surface tension and viscosity. The corresponding rather simple linear regression equations which include one, two or three parameters correspondingly have been obtained. The predictive ability of the equations has been investigated using internal validation tests. The test by leave-one-out (LOO) validation and Y‑scrambling evaluate the obtained equations as adequate. For instance, for the regression model for boiling point the best equation characterizes by determination coefficients R2 = 0.943, with LOO procedure – Q2 = 0.918, while for the Y-scrambling test Q2y-scr<0.3 basically. It is shown that all the abovementioned molecular properties in iterated line graph approach can be effectively described by commonly used topological indices. Namely almost every randomly selected topological index can give adequate equation. Effectiveness is demonstrated on the example of Zagreb group indices. Also essential effectiveness and rather universal applicability of the so-called “forgotten” index (ZM3) was demonstrated.

Topological aspects of some dendrimer structures

2018 ◽  
Vol 7 (2) ◽  
pp. 123-129 ◽  
Author(s):  
Adnan Aslam ◽  
Muhammad Kamran Jamil ◽  
Wei Gao ◽  
Waqas Nazeer
Keyword(s):  
Self Assembly ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Molecular Topology ◽  
Zinc Porphyrin ◽  
Physico Chemical ◽  
Randić Connectivity Index ◽  
Atom Bond

AbstractA numerical number associated to the molecular graphGthat describes its molecular topology is called topological index. In the study ofQSARandQSPR, topological indices such as atom-bond connectivity index, Randić connectivity index, geometric index, etc. help to predict many physico-chemical properties of the chemical compound under study. Dendrimers are macromolecules and have many applications in chemistry, especially in self-assembly procedures and host-guest reactions. The aim of this report is to compute degree-based topological indices, namely the fourth atom-bond connectivity index and fifth geometric arithmetic index of poly propyl ether imine, zinc porphyrin, and porphyrin dendrimers.

scholarly journals On topological properties of dominating David derived networks

2016 ◽  
Vol 94 (2) ◽  
pp. 137-148 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Qudair Baig ◽  
Haidar Ali
Keyword(s):  
Interconnection Networks ◽  
Network Science ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Topology ◽  
Topological Properties ◽  
Graph Invariant ◽  
Physico Chemical ◽  
Atom Bond

Topological indices are numerical parameters of a graph that characterize its molecular topology and are usually graph invariant. In a QSAR/QSPR study, the physico-chemical properties and topological indices such as the 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 important area of research. All of the studied interconnection networks in this paper are constructed by the Star of David network. In this paper, we study the general Randić, first Zagreb, ABC, GA, ABC4 and GA5, indices for the first, second, and third types of dominating David derived networks and give closed formulas of these indices for these networks. These results are useful in network science to understand the underlying topologies of these networks.

scholarly journals COMPUTING TOPOLOGICAL INDICES OF SiO2 LAYER STRUCTURE AND BENZENOID SERIES

2019 ◽  
Vol 49 (4) ◽  
pp. 219-224
Author(s):  
M. H. Muhammad ◽  
Juan Luis Garcia Guirao ◽  
N. A. Rehman ◽  
M. K. Siddiqui
Keyword(s):  
Strain Energy ◽  
Layer Structure ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Sio2 Layer ◽  
Physico Chemical ◽  
Forgotten Index ◽  
Map Operations

A molecular graph can be transformed using map operations, one of these, named Capra, being defined by Diudea (2005). Topological indices are closely related to the toxicological, physicochemical, pharmacological properties of a chemical compound. These topological indices correlate certain physico-chemical properties like boiling point, stability and strain energy of chemical compounds. In this paper, we focus on the Silicate SiO2 layer structure and the structure of Capra-designed planar benzenoid series , (). We determined Zagreb type indices, Forgotten index, Augmented index and Balaban index for these structures.

scholarly journals Eccentricity based topological indices of siloxane and POPAM dendrimers

2020 ◽  
Vol 43 (1) ◽  
pp. 92-98
Author(s):  
Muhammad Azhar Iqbal ◽  
Muhammad Imran ◽  
Muhammad Asad Zaighum
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Descriptors ◽  
Physico Chemical ◽  
Early Drug

AbstractA massive of early drug tests indicates that there is some strong inner connections among the bio-medical and pharmacology properties of nanostar dendrimers and their molecular structures. Topological descriptors are presented as fundamentally transforming a molecular graph into a number. There exist various categories of such descriptors particularly those descriptors that based on edge and vertex distances. Topological descriptors are exercised for designing biological, physico-chemical, toxicological, pharmacologic and other characteristics of chemical compounds. In this paper, we study infinite classes of siloxane and POPAM dendrimers and derive their Zagreb eccentricity indices, eccentric-connectivity and total-eccentricity indices.

scholarly journals Topological Indices of mth Chain Silicate Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 42 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Kashif Shafiq ◽  
Haidar Ali ◽  
Asim Naseem ◽  
Nayab Maryam ◽  
...  
Keyword(s):  
Biological Activity ◽  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Numerical Representation ◽  
Topological Descriptor ◽  
Physico Chemical ◽  
Chain Silicate ◽  
Atom Bond

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, and biological activity are determined by the chemical applications of graph theory. The biological activity of chemical compounds can be constructed by the help of topological indices such as atom-bond connectivity (ABC), Randić, and geometric arithmetic (GA). In this paper, Randić, atom bond connectivity (ABC), Zagreb, geometric arithmetic (GA), ABC4, and GA5 indices of the mth chain silicate S L ( m , n ) network are determined.

scholarly journals On Distance-Based Topological Descriptors of Chemical Interconnection Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Min Hu ◽  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Bilal Ali ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Interconnection Networks ◽  
Topological Index ◽  
Chemical Properties ◽  
Topological Descriptors ◽  
Silicate Network ◽  
Pi Index ◽  
Szeged Index ◽  
Physico Chemical ◽  
Chain Silicate ◽  
First Time

Structure-based topological descriptors of chemical networks enable us the prediction of physico-chemical properties and the bioactivities of compounds through QSAR/QSPR methods. Topological indices are the numerical values to represent a graph which characterises the graph. One of the latest distance-based topological index is the Mostar index. In this paper, we study the Mostar index, Szeged index, PI index, ABC GG index, and NGG index, for chain oxide network COX n , chain silicate network CS n , ortho chain S n , and para chain Q n , for the first time. Moreover, analytically closed formulae for these structures are determined.

scholarly journals Molecular topological invariants of certain chemical networks

2021 ◽  
Vol 44 (1) ◽  
pp. 141-149
Author(s):  
Syed Ahtsham Ul Haq Bokhary ◽  
Muhammad Imran ◽  
Shehnaz Akhter ◽  
Sadia Manzoor
Keyword(s):  
Chemical Compounds ◽  
Topological Descriptors ◽  
Discrete Mathematics ◽  
Chemical Characteristics ◽  
Topological Invariants ◽  
Molecular Topology ◽  
Graph Invariants ◽  
Physico Chemical ◽  
Structure Relationship ◽  
Atom Bond

Abstract Topological descriptors are the graph invariants that are used to explore the molecular topology of the molecular/chemical graphs. In QSAR/QSPR research, physico-chemical characteristics and topological invariants including Randić, atom-bond connectivity, and geometric arithmetic invariants are utilized to corelate and estimate the structure relationship and bioactivity of certain chemical compounds. Graph theory and discrete mathematics have discovered an impressive utilization in the area of research. In this article, we investigate the valency-depended invariants for certain chemical networks like generalized Aztec diamonds and tetrahedral diamond lattice. Moreover, the exact values of invariants for these categories of chemical networks are derived.

Graph Neural Networks for Prediction of Fuel Ignition Quality

2020 ◽  
Author(s):  
Artur Schweidtmann ◽  
Jan Rittig ◽  
Andrea König ◽  
Martin Grohe ◽  
Alexander Mitsos ◽  
...  
Keyword(s):  
Neural Networks ◽  
Octane Number ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Graph Representation ◽  
Structure Property ◽  
Oxygenated Hydrocarbons ◽  
Physico Chemical ◽  
Ignition Quality ◽  
Graph Neural Networks

<div>Prediction of combustion-related properties of (oxygenated) hydrocarbons is an important and challenging task for which quantitative structure-property relationship (QSPR) models are frequently employed. Recently, a machine learning method, graph neural networks (GNNs), has shown promising results for the prediction of structure-property relationships. GNNs utilize a graph representation of molecules, where atoms correspond to nodes and bonds to edges containing information about the molecular structure. More specifically, GNNs learn physico-chemical properties as a function of the molecular graph in a supervised learning setup using a backpropagation algorithm. This end-to-end learning approach eliminates the need for selection of molecular descriptors or structural groups, as it learns optimal fingerprints through graph convolutions and maps the fingerprints to the physico-chemical properties by deep learning. We develop GNN models for predicting three fuel ignition quality indicators, i.e., the derived cetane number (DCN), the research octane number (RON), and the motor octane number (MON), of oxygenated and non-oxygenated hydrocarbons. In light of limited experimental data in the order of hundreds, we propose a combination of multi-task learning, transfer learning, and ensemble learning. The results show competitive performance of the proposed GNN approach compared to state-of-the-art QSPR models making it a promising field for future research. The prediction tool is available via a web front-end at www.avt.rwth-aachen.de/gnn.</div>

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