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The Generation of Fullerenes

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Applied Mathematics & Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium
Applied Mathematics & Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium
§ Research School of Computer Science, Australian National University, ACT 0200, Australia
Cite this: J. Chem. Inf. Model. 2012, 52, 11, 2910–2918
Publication Date (Web):September 30, 2012
https://doi.org/10.1021/ci3003107
Copyright © 2012 American Chemical Society

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    Abstract

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    We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes – fullgen – and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are Hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.

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    5. Kris Coolsaet, Sven D’hondt, Jan Goedgebeur. House of Graphs 2.0: A database of interesting graphs and more. Discrete Applied Mathematics 2023, 325 , 97-107. https://doi.org/10.1016/j.dam.2022.10.013
    6. D. G. Stepenshchikov, S. M. Aksenov. ON THE EXISTENCE OF FULLERENES WITH A GIVEN SYMMETRY GROUP. Journal of Structural Chemistry 2022, 63 (12) , 2083-2094. https://doi.org/10.1134/S0022476622120198
    7. František Kardoš. Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes. SIAM Review 2022, 64 (2) , 425-465. https://doi.org/10.1137/22M1476915
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    9. Mariia Myronova. On symmetry breaking of dual polyhedra of non-crystallographic group H 3. Acta Crystallographica Section A Foundations and Advances 2021, 77 (4) , 296-316. https://doi.org/10.1107/S2053273321002254
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    11. Benjamin Heuser, Kurt V. Mikkelsen, James E. Avery. Simulating fullerene polyhedral formation from planar precursors. Physical Chemistry Chemical Physics 2021, 23 (11) , 6561-6573. https://doi.org/10.1039/D0CP04901H
    12. N. Yu. Erokhovets. Theory of Families of Polytopes: Fullerenes and Pogorelov Polytopes. Moscow University Mathematics Bulletin 2021, 76 (2) , 83-95. https://doi.org/10.3103/S0027132221020042
    13. Artur Bille, Victor Buchstaber, Evgeny Spodarev. Spectral clustering of combinatorial fullerene isomers based on their facet graph structure. Journal of Mathematical Chemistry 2021, 59 (1) , 264-288. https://doi.org/10.1007/s10910-020-01193-4
    14. Qingnan Zhao, Wei Song, Bing Zhao, Bai Yang. Spectroscopic studies of the optical properties of carbon dots: recent advances and future prospects. Materials Chemistry Frontiers 2020, 4 (2) , 472-488. https://doi.org/10.1039/C9QM00592G
    15. František Kardoš. A Computer-Assisted Proof of the Barnette--Goodey Conjecture: Not Only Fullerene Graphs Are Hamiltonian. SIAM Journal on Discrete Mathematics 2020, 34 (1) , 62-100. https://doi.org/10.1137/140984737
    16. A. A. Egorov, A Yu. Vesnin. On correlation of hyperbolic volumes of fullerenes with their properties. Computational and Mathematical Biophysics 2020, 8 (1) , 150-167. https://doi.org/10.1515/cmb-2020-0108
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    22. James Emil Avery. Wave equations without coordinates I: fullerenes. Rendiconti Lincei. Scienze Fisiche e Naturali 2018, 29 (3) , 609-621. https://doi.org/10.1007/s12210-018-0717-4
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    26. V M Buchstaber, N Yu Erokhovets. Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes. Izvestiya: Mathematics 2017, 81 (5) , 901-972. https://doi.org/10.1070/IM8665
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    28. Victor M. Buchstaber, Nikolay Yu. Erokhovets. Finite sets of operations sufficient to construct any fullerene from C 20. Structural Chemistry 2017, 28 (1) , 225-234. https://doi.org/10.1007/s11224-016-0885-8
    29. Виктор Матвеевич Бухштабер, Victor Matveevich Buchstaber, Николай Юрьевич Ероховец, Nikolai Yur'evich Erokhovets. Конструкции семейств трехмерных многогранников, характеристические фрагменты фуллеренов и многогранники Погорелова. Известия Российской академии наук. Серия математическая 2017, 81 (5) , 15-91. https://doi.org/10.4213/im8665
    30. Jan Goedgebeur, Brendan D. McKay. Recursive generation of IPR fullerenes. Journal of Mathematical Chemistry 2015, 53 (8) , 1702-1724. https://doi.org/10.1007/s10910-015-0513-7
    31. Alfredo García, Ferran Hurtado, Matias Korman, Inês Matos, Maria Saumell, Rodrigo I. Silveira, Javier Tejel, Csaba D. Tóth. Geometric Biplane Graphs I: Maximal Graphs. Graphs and Combinatorics 2015, 31 (2) , 407-425. https://doi.org/10.1007/s00373-015-1546-1
    32. Peter Schwerdtfeger, Lukas N Wirz, James Avery. The topology of fullerenes. WIREs Computational Molecular Science 2015, 5 (1) , 96-145. https://doi.org/10.1002/wcms.1207
    33. Modjtaba Ghorbani, Elaheh Bani-Asadi. Remarks on characteristic coefficients of fullerene graphs. Applied Mathematics and Computation 2014, 230 , 428-435. https://doi.org/10.1016/j.amc.2013.12.074
    34. Jerzy Cioslowski. Note on the asymptotic isomer count of large fullerenes. Journal of Mathematical Chemistry 2014, 52 (1) , 1-5. https://doi.org/10.1007/s10910-013-0263-3
    35. Peter Schwerdtfeger, Lukas Wirz, James Avery. Program Fullerene: A software package for constructing and analyzing structures of regular fullerenes. Journal of Computational Chemistry 2013, 34 (17) , 1508-1526. https://doi.org/10.1002/jcc.23278
    36. P.W. Fowler, B.T. Pickup, T.Z. Todorova, R. De Los Reyes, I. Sciriha. Omni-conducting fullerenes. Chemical Physics Letters 2013, 568-569 , 33-35. https://doi.org/10.1016/j.cplett.2013.03.022