Fowler, P.W. orcid.org/0000-0003-2106-1104, Pisanski, T. and Basic, N. (2021) Charting the space of chemical nut graphs. Match: Communications in Mathematical and in Computer Chemistry, 86 (3). pp. 519-538. ISSN 0340-6253
Abstract
Molecular graphs of unsaturated carbon frameworks or hydrocarbons pruned of hydrogen atoms, are chemical graphs. A chemical graph is a connected simple graph of maximum degree 3 or less. A nut graph is a connected simple graph with a singular adjacency matrix that has one zero eigenvalue and a non-trivial kernel eigenvector without zero entries. Nut graphs have no vertices of degree 1: They are leaess. The intersection of these two sets, the chemical nut graphs, is of interest in applications in chemistry and molecular physics, corresponding to structures with fully distributed radical reactivity and omniconducting behaviour at the Fermi level. A chemical nut graph consists of v2 _ 0 vertices of degree 2 and an even number, v3 > 0, of vertices of degree 3. With the aid of systematic local constructions that produce larger nut graphs from smaller, the combinations (v3; v2) corresponding to realisable chemical nut graphs are characterised. Apart from a _inite set of small cases, and two simply de_ned in_inite series, all combinations (v3; v2) with even values of v3 > 0 are realisable as chemical nut graphs. Of these combinations, only (20; 0) cannot be realised by a planar chemical nut graph. The main result characterises the ranges of edge counts for chemical nut graphs of all orders n, and hence leads to a characterisation of the chemical formulas of all possible conjugated hydrocarbons corresponding to chemical nut graphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Match. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Chemistry (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Nov 2021 09:25 |
Last Modified: | 16 Nov 2021 09:25 |
Published Version: | https://match.pmf.kg.ac.rs/content86n3.htm |
Status: | Published |
Publisher: | University of Kragujevac |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180445 |