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Mathematics
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Recent Advances in Chemical Graph Theory and Their Applications
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Recent Advances in Chemical Graph Theory and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 21937

Special Issue Editors

Prof. Dr. Petra Zigert Pletersek

E-Mail Website
Guest Editor
Faculty of Chemistry and Chemical Engineering, Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
Interests: chemical graph theory; matchings; resonance graphs; topological indices; QSPR analysis; nanostructures
Dr. Niko Tratnik

E-Mail Website
Guest Editor
Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
Interests: chemical graph theory; topological indices; resonance graphs; complex networks

Special Issue Information

Dear Colleagues,

Since the seminal paper of the American chemist Harold Wiener in 1947, many numerical quantities of graphs have been introduced and extensively studied in order to describe various physicochemical properties. Such graph invariants are most commonly referred to as topological indices and are often defined using degrees of vertices, distances between vertices, eigenvalues, symmetries, and many other properties of graphs. It is desirable for a topological index to also be a molecular descriptor. In order to establish the connection between topological indices and the properties or activities of studied compounds, quantitative structure–activity relationships (QSAR) and quantitative structure–property relationships (QSPR) must be performed. This enables the process of finding new compounds with desired properties in silico instead of in vitro.

There are well studied groups of molecules composed of carbon and hydrogen atoms, but modeling of more complex heteroatomic compounds is much more challenging. On the other hand, topological indices have also found enormous applications in rapidly growing research of complex networks, which include communications networks, social networks, biological networks, etc. In such networks, these indices are used as measures for various structural properties.

The purpose of this Special Issue is to report and review recent developments concerning mathematical properties, methods of calculations, and applications of topological indices in any area of interest. Moreover, papers on other topics in chemical graph theory are also welcome.

Prof. Dr. Petra Zigert Pletersek
Dr. Niko Tratnik
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Topological indices
  • Molecular descriptors
  • Methods of calculations
  • Algorithms
  • QSP(A)R analysis
  • Molecular graphs
  • Complex molecules
  • Nanostructures
  • Different measures in networks

Published Papers (5 papers)

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Research

16 pages, 1139 KiB  
Article
Weighted Wiener Indices of Molecular Graphs with Application to Alkenes and Alkadienes
by Simon Brezovnik, Niko Tratnik and Petra Žigert Pleteršek
Mathematics 2021, 9(2), 153; https://0-doi-org.brum.beds.ac.uk/10.3390/math9020153 - 12 Jan 2021
Cited by 2 | Viewed by 7561
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Recent Advances in Chemical Graph Theory and Their Applications)
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11 pages, 257 KiB  
Article
Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree
by Aleksander Vesel
Mathematics 2021, 9(2), 142; https://0-doi-org.brum.beds.ac.uk/10.3390/math9020142 - 11 Jan 2021
Cited by 1 | Viewed by 3601
Abstract
The Hosoya index of a graph is defined as the total number of its independent edge sets. This index is an important example of topological indices, a molecular-graph based structure descriptor that is of significant interest in combinatorial chemistry. The Hosoya index inspires [...] Read more.
The Hosoya index of a graph is defined as the total number of its independent edge sets. This index is an important example of topological indices, a molecular-graph based structure descriptor that is of significant interest in combinatorial chemistry. The Hosoya index inspires the introduction of a matrix associated with a molecular acyclic graph called the Hosoya matrix. We propose a simple linear-time algorithm, which does not require pre-processing, to compute the Hosoya index of an arbitrary tree. A similar approach allows us to show that the Hosoya matrix can be computed in constant time per entry of the matrix. Full article
(This article belongs to the Special Issue Recent Advances in Chemical Graph Theory and Their Applications)
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19 pages, 4495 KiB  
Article
Chemical Graph Theory for Property Modeling in QSAR and QSPR—Charming QSAR & QSPR
by Paulo C. S. Costa, Joel S. Evangelista, Igor Leal and Paulo C. M. L. Miranda
Mathematics 2021, 9(1), 60; https://0-doi-org.brum.beds.ac.uk/10.3390/math9010060 - 29 Dec 2020
Cited by 14 | Viewed by 4508
Abstract
Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR) are mathematical models for the prediction of the chemical, physical or biological properties of chemical compounds. Usually, they are based on structural (grounded on fragment contribution) or calculated (centered on QSAR three-dimensional (QSAR-3D) or [...] Read more.
Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR) are mathematical models for the prediction of the chemical, physical or biological properties of chemical compounds. Usually, they are based on structural (grounded on fragment contribution) or calculated (centered on QSAR three-dimensional (QSAR-3D) or chemical descriptors) parameters. Hereby, we describe a Graph Theory approach for generating and mining molecular fragments to be used in QSAR or QSPR modeling based exclusively on fragment contributions. Merging of Molecular Graph Theory, Simplified Molecular Input Line Entry Specification (SMILES) notation, and the connection table data allows a precise way to differentiate and count the molecular fragments. Machine learning strategies generated models with outstanding root mean square error (RMSE) and R2 values. We also present the software Charming QSAR & QSPR, written in Python, for the property prediction of chemical compounds while using this approach. Full article
(This article belongs to the Special Issue Recent Advances in Chemical Graph Theory and Their Applications)
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7 pages, 210 KiB  
Article
All Pairs of Pentagons in Leapfrog Fullerenes Are Nice
by Tomislav Došlić
Mathematics 2020, 8(12), 2135; https://0-doi-org.brum.beds.ac.uk/10.3390/math8122135 - 1 Dec 2020
Cited by 7 | Viewed by 1763
Abstract
A subgraph H of a graph G with perfect matching is nice if G−V(H) has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as [...] Read more.
A subgraph H of a graph G with perfect matching is nice if G−V(H) has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution, we consider fullerene graphs arising from smaller fullerenes via the leapfrog transformation, and show that in such graphs, each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs. Full article
(This article belongs to the Special Issue Recent Advances in Chemical Graph Theory and Their Applications)
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16 pages, 849 KiB  
Article
On Three Constructions of Nanotori
by Vesna Andova, Pavel Dimovski, Martin Knor and Riste Škrekovski
Mathematics 2020, 8(11), 2036; https://0-doi-org.brum.beds.ac.uk/10.3390/math8112036 - 16 Nov 2020
Cited by 4 | Viewed by 1738
Abstract
There are three different approaches for constructing nanotori in the literature: one with three parameters suggested by Altshuler, another with four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks [...] Read more.
There are three different approaches for constructing nanotori in the literature: one with three parameters suggested by Altshuler, another with four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks of computer science known under the name generalized honeycomb tori. Altshuler showed that his method gives all non-isomorphic nanotori, but this was not known for the other two constructions. Here, we show that these three approaches are equivalent and give explicit formulas that convert parameters of one construction into the parameters of the other two constructions. As a consequence, we obtain that the other two approaches also construct all nanotori. The four parameters construction is mainly used in chemistry and physics to describe carbon nanotori molecules. Some properties of the nanotori can be predicted from these four parameters. We characterize when two different quadruples define isomorphic nanotori. Even more, we give an explicit form of all isomorphic nanotori (defined with four parameters). As a consequence, infinitely many 4-tuples correspond to each nanotorus; this is due to redundancy of having an “extra” parameter, which is not a case with the other two constructions. This result significantly narrows the realm of search of the molecule with desired properties. The equivalence of these three constructions can be used for evaluating different graph measures as topological indices, etc. Full article
(This article belongs to the Special Issue Recent Advances in Chemical Graph Theory and Their Applications)
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