Extremal Chemical Trees

Avariety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W, the largest graph eigenvalue λ1, the connectivity index χ, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W, λ1, E, and Z, whereas the analogous problem for χ was solved earlier. Among chemical trees with 5, 6, 7, and 3k + 2 vertices, k = 2, 3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k + 1 vertices, k = 3, 4..., one tree has minimum W and maximum λ1 and another minimum E and Z.

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Graph Neural Networks for Prediction of Fuel Ignition Quality

10.26434/chemrxiv.12280325.v1 ◽

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

Kharkov University Bulletin Chemical Series ◽

10.26565/2220-637x-2019-32-02 ◽

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.

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Effect of a Ring onto Values of Eigenvalue–Based Molecular Descriptors

Symmetry ◽

10.3390/sym13081515 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1515

Author(s):

Izudin Redžepović ◽

Slavko Radenković ◽

Boris Furtula

Keyword(s):

Molecular Descriptors ◽

Biological Activities ◽

Molecular Graph ◽

Chemical Properties ◽

Estrada Index ◽

Molecular Features ◽

Physico Chemical ◽

Graph Energy ◽

Structural Details ◽

The Impact

The eigenvalues of the characteristic polynomial of a graph are sensitive to its symmetry-related characteristics. Within this study, we have examined three eigenvalue–based molecular descriptors. These topological molecular descriptors, among others, are gathering information on the symmetry of a molecular graph. Furthermore, they are being ordinarily employed for predicting physico–chemical properties and/or biological activities of molecules. It has been shown that these indices describe well molecular features that are depending on fine structural details. Therefore, revealing the impact of structural details on the values of the eigenvalue–based topological indices should give a hunch how physico–chemical properties depend on them as well. Here, an effect of a ring in a molecule on the values of the graph energy, Estrada index and the resolvent energy of a graph is examined.

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Choosing the exponent in the definition of the connectivity index

Journal of the Serbian Chemical Society ◽

10.2298/jsc0109605g ◽

2001 ◽

Vol 66 (9) ◽

pp. 605-611 ◽

Cited By ~ 13

Author(s):

Ivan Gutman ◽

Mirko Lepovic

Keyword(s):

Carbon Atom ◽

Topological Index ◽

Organic Molecules ◽

Molecular Graph ◽

Chemical Properties ◽

Connectivity Index ◽

Physico Chemical ◽

Definition Of ◽

Molecular Branching ◽

Suitable Measure

Let ?v denote the degree of the vertex v of a molecular graph G. Then the connectivity index of G is defined as C (?) = G (?,C) = ? (?u?v)?, where the summation goes over all pairs of adjacent vertices. The exponent ? is usually chosen to be equal to -1/2, but other options were considered as well, especially ?=-1. We show that whereas C(-1/2) is a suitable measure of branching of the carbon-atom skeleton of organic molecules, and thus applicable as a topological index for modeling physico-chemical properties of the respective compounds, this is not the case with C(-1). The value of ? is established, beyond which C(?) fails to correctly reflect molecular branching.

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Graph Neural Networks for Prediction of Fuel Ignition Quality

10.26434/chemrxiv.12280325 ◽

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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Weighted Wiener Indices of Molecular Graphs with Application to Alkenes and Alkadienes

Mathematics ◽

10.3390/math9020153 ◽

2021 ◽

Vol 9 (2) ◽

pp. 153

Author(s):

Simon Brezovnik ◽

Niko Tratnik ◽

Petra Žigert Pleteršek

Keyword(s):

Linear Regression Analysis ◽

Chemical Properties ◽

Wiener Index ◽

Topological Indices ◽

The Other ◽

Multiple Bonds ◽

Saturated Hydrocarbons ◽

Simple Graphs ◽

Boiling Points ◽

Physico Chemical

There exist many topological indices that are calculated on saturated hydrocarbons since they can be easily modelled by simple graphs. On the other hand, it is more challenging to investigate topological indices for hydrocarbons with multiple bonds. The purpose of this paper is to introduce a simple model that gives good results for predicting physico-chemical properties of alkenes and alkadienes. In particular, we are interested in predicting boiling points of these molecules by using the well known Wiener index and its weighted versions. By performing the non-linear regression analysis we predict boiling points of alkenes and alkadienes.

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On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽

10.3390/sym10080320 ◽

2018 ◽

Vol 10 (8) ◽

pp. 320 ◽

Cited By ~ 12

Author(s):

Young Kwun ◽

Abaid Virk ◽

Waqas Nazeer ◽

M. Rehman ◽

Shin Kang

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Compound ◽

Zagreb Indices ◽

Silicon Carbon ◽

Physico Chemical ◽

Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

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On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

10.20944/preprints201806.0066.v1 ◽

2018 ◽

Author(s):

Young Chel Kwun ◽

Abaid ur Rehman Virk ◽

Waqas Nazeer ◽

Shin Min Kang

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Compound ◽

Silicon Carbon ◽

Physico Chemical ◽

Structure Research

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q].

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Wiener Indices and Molecular Surfaces

Zeitschrift für Naturforschung A ◽

10.1515/zna-1995-0707 ◽

1995 ◽

Vol 50 (7) ◽

pp. 669-671 ◽

Cited By ~ 7

Author(s):

Ivan Gutmana ◽

Tamás Körtvélyesi

Keyword(s):

Volume Ratio ◽

Wiener Index ◽

Molecular Surface ◽

Molecular Volume ◽

Saturated Hydrocarbons ◽

Molecular Surfaces ◽

Physico Chemical ◽

First Time

A correlation between the Wiener index (W) and the molecular surface of the respective alkane is established for the first time. This correlation is curvilinear and not particularly good. W is only weakly correlated to molecular volume of saturated hydrocarbons and does not reflect at all their surface-to-volume ratio. By this a long-existing controversy concerning the physico-chemical interpretation of W is resolved.

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