scholarly journals Computing the Omega polynomial of an infinite family of the linear parallelogram P(n,m)

2006 ◽  
Vol 2 (2) ◽  
pp. 106-109
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Molecular Graph ◽  
Infinite Family ◽  
Benzenoid Graph ◽  
Omega Polynomial

Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges. The Omega polynomial Ω(G,x) was introduced by Diudea in 2006 and this defined as  where m(G,c) the number of qoc strips of length c. In this paper, we compute the omega polynomial of an infinite family of the linear parallelogram P(n,n) of benzenoid graph.

Computing the Theta Polynomial Θ(G, x) and the Theta Index Θ(G) of Titania Nanotubes TiO2(m, n)

2017 ◽  
Vol 14 (1) ◽  
pp. 715-717
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Mohammad R Farahani ◽  
Muhammad Imran ◽  
Muhammad K Jamil
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Infinite Family ◽  
Titania Nanotubes ◽  
Chemical Graph ◽  
First Derivative ◽  
Chemical Graph Theory ◽  
Omega Polynomial ◽  
Definition Of ◽  
First Time

Let G = (V,E) be a simple connected molecular graph in chemical graph theory, where the vertex/atom set and edge/bond set of G denoted by V(G) and E(G), respectively and its vertices correspond to the atoms and the edges correspond to the bonds. Two counting polynomials the “Omega Ω(G,x) and Theta Θ(G,x)” polynomials of a molecular graph G were defined by Diudea as Ω(G,x) = ΣeE(G) xn(E) and Θ(G,x) = ΣeE(G) xn(E), where n(E) denotes the number of edges co-distant with the edge E. From definition of these counting polynomials, we can obtain the Theta polynomial by inserting the coefficient n(E) in the Omega polynomial. Then the Theta index will be the first derivative of the Theta polynomial Θ(G,x) evaluated at x = 1. The goal of this paper is to compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of an infinite family of the Titania Nanotubes TiO2(m,n) for the first time.

Computing a Counting Polynomial of an Infinite Family of Linear Polycene Parallelogram Benzenoid Graph P(a,b)

2007 ◽  
Vol 3 (1) ◽  
pp. 186-190
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Infinite Family ◽  
Benzenoid Graph ◽  
First Derivative ◽  
Omega Polynomial ◽  
Counting Polynomial ◽  
First Time

Omega polynomial was defined by M.V. Diudea in 2006 as  where the number of edges co-distant with e is denoted by n(e). One can obtain Theta Θ, Sadhana Sd and Pi Π polynomials by replacing xn(e) with n(e)xn(e), x|E|-n(e) and n(e)x|E|-n(e) in Omega polynomial, respectively. Then Theta Θ, Sadhana Sd and Pi Π indices will be the first derivative of Θ(x), Sd(x) and Π(x) evaluated at x=1. In this paper, Pi Π(G,x) polynomial and Pi Π(G) index of an infinite family of linear polycene parallelogram benzenoid graph P(a,b) are computed for the first time.

scholarly journals On Connectivity Indices of an Infinite Family of the Linear Parallelogram of Benzenoid Graph

2015 ◽  
Vol 54 ◽  
pp. 131-134
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Infinite Family ◽  
Infinite Class ◽  
Benzenoid Graph ◽  
Connectivity Indices ◽  
Atom Bond

A topological index of a graph G is a numeric quantity related to G which is describe molecular graph G. In this paper the Atom Bond Connectivity (ABC) and Geometric-Arithmetic (GA) indices of an infinite class of the linear parallelogram of benzenoid graph.

scholarly journals Wiener Index of Edge Thorny Graphs of Catacondensed Benzenoids

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 467
Author(s):  
Andrey A. Dobrynin ◽  
Ali Iranmanesh
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Perfect Matching ◽  
Molecular Graph ◽  
Wiener Index ◽  
Benzenoid Graph ◽  
Polycyclic Aromatic ◽  
Distance Properties ◽  
Sum Of Distances

The Wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. Benzenoid graphs include molecular graphs of polycyclic aromatic hydrocarbons. An edge thorny graph G is constructed from a catacondensed benzenoid graph H by attaching new graphs to edges of a perfect matching of H. A formula for the Wiener index of G is derived. The index of the resulting graph does not contain distance characteristics of elements of H and depends on the Wiener index of H and distance properties of the attached graphs.

scholarly journals The Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk

2015 ◽  
Vol 12 (1) ◽  
pp. 3934-3939 ◽  
Author(s):  
Wei Gao ◽  
MOHAMMAD REZA FARAHANI
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Positive Integer ◽  
Aromatic Hydrocarbons ◽  
Molecular Graph ◽  
Integer Number ◽  
Polycyclic Aromatic ◽  
Omega Polynomial

The omega polynomial Ω(G,x), for counting qoc strips in molecular graph G was defined by Diudea as  with m(G,c), being the number of qoc strips of length c. The Theta polynomial Θ(G,x) and the Theta index Θ(G) of a molecular graph G were defined as Θ(G,x)= and Θ(G)=, respectively.In this paper, we compute the Theta polynomial Θ(G,x) and the Theta index Θ(G) of molecular graph Polycyclic Aromatic Hydrocarbons PAHk, for all positive integer number k. 

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>

SAMPL6 Challenge Results from pKa Predictions Based on a General Gaussian Process Model

2018 ◽  
Author(s):  
Caitlin C. Bannan ◽  
David Mobley ◽  
A. Geoff Skillman
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Molecular Graph ◽  
Gaussian Process Regression ◽  
Ionization State ◽  
Training Set ◽  
Physiochemical Properties ◽  
Quantile Plots ◽  
Physical And Chemical ◽  
Good Agreement

<div>A variety of fields would benefit from accurate pK<sub>a</sub> predictions, especially drug design due to the affect a change in ionization state can have on a molecules physiochemical properties.</div><div>Participants in the recent SAMPL6 blind challenge were asked to submit predictions for microscopic and macroscopic pK<sub>a</sub>s of 24 drug like small molecules.</div><div>We recently built a general model for predicting pK<sub>a</sub>s using a Gaussian process regression trained using physical and chemical features of each ionizable group.</div><div>Our pipeline takes a molecular graph and uses the OpenEye Toolkits to calculate features describing the removal of a proton.</div><div>These features are fed into a Scikit-learn Gaussian process to predict microscopic pK<sub>a</sub>s which are then used to analytically determine macroscopic pK<sub>a</sub>s.</div><div>Our Gaussian process is trained on a set of 2,700 macroscopic pK<sub>a</sub>s from monoprotic and select diprotic molecules.</div><div>Here, we share our results for microscopic and macroscopic predictions in the SAMPL6 challenge.</div><div>Overall, we ranked in the middle of the pack compared to other participants, but our fairly good agreement with experiment is still promising considering the challenge molecules are chemically diverse and often polyprotic while our training set is predominately monoprotic.</div><div>Of particular importance to us when building this model was to include an uncertainty estimate based on the chemistry of the molecule that would reflect the likely accuracy of our prediction. </div><div>Our model reports large uncertainties for the molecules that appear to have chemistry outside our domain of applicability, along with good agreement in quantile-quantile plots, indicating it can predict its own accuracy.</div><div>The challenge highlighted a variety of means to improve our model, including adding more polyprotic molecules to our training set and more carefully considering what functional groups we do or do not identify as ionizable. </div>

Multi-Resolution Autoregressive Graph-to-Graph Translation for Molecules

2019 ◽  
Author(s):  
Wengong Jin ◽  
Regina Barzilay ◽  
Tommi S Jaakkola
Keyword(s):  
Drug Discovery ◽  
State Of The Art ◽  
Molecular Graph ◽  
Biochemical Properties ◽  
Large Margin ◽  
Previous State ◽  
Translation Methods ◽  
Atom Level ◽  
Precursor Molecules ◽  
Prior State

The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on graph-to-graph translation methods for molecular optimization. In particular, we realize coherent multi-resolution representations by interweaving trees over substructures with the atom-level encoding of the original molecular graph. Moreover, our graph decoder is fully autoregressive, and interleaves each step of adding a new substructure with the process of resolving its connectivity to the emerging molecule. We evaluate our model on multiple molecular optimization tasks and show that our model outperforms previous state-of-the-art baselines by a large margin.

The Application of the Combination of Monte Carlo Optimization Method based QSAR Modeling and Molecular Docking in Drug Design and Development

2020 ◽  
Vol 20 (14) ◽  
pp. 1389-1402 ◽  
Author(s):  
Maja Zivkovic ◽  
Marko Zlatanovic ◽  
Nevena Zlatanovic ◽  
Mladjan Golubović ◽  
Aleksandar M. Veselinović
Keyword(s):  
Monte Carlo ◽  
Molecular Docking ◽  
Computer Calculation ◽  
Molecular Graph ◽  
Optimization Method ◽  
Docking Studies ◽  
Optimization Approach ◽  
Qsar Modeling ◽  
Monte Carlo Optimization ◽  
Molecular Docking Studies

In recent years, one of the promising approaches in the QSAR modeling Monte Carlo optimization approach as conformation independent method, has emerged. Monte Carlo optimization has proven to be a valuable tool in chemoinformatics, and this review presents its application in drug discovery and design. In this review, the basic principles and important features of these methods are discussed as well as the advantages of conformation independent optimal descriptors developed from the molecular graph and the Simplified Molecular Input Line Entry System (SMILES) notation compared to commonly used descriptors in QSAR modeling. This review presents the summary of obtained results from Monte Carlo optimization-based QSAR modeling with the further addition of molecular docking studies applied for various pharmacologically important endpoints. SMILES notation based optimal descriptors, defined as molecular fragments, identified as main contributors to the increase/ decrease of biological activity, which are used further to design compounds with targeted activity based on computer calculation, are presented. In this mini-review, research papers in which molecular docking was applied as an additional method to design molecules to validate their activity further, are summarized. These papers present a very good correlation among results obtained from Monte Carlo optimization modeling and molecular docking studies.

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