The Generation of Fullerenes
Copyright policy )The Generation of Fullerenes
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.
21 pages; added a note
- KU Leuven Belgium
- Australian National University Australia
- Ghent University Belgium
FOS: Computer and information sciences, Technology, Discrete Mathematics (cs.DM), Chemistry, Multidisciplinary, Medicinal & Biomolecular Chemistry, FOS: Physical sciences, Chemistry, Medicinal, GRAPHS, FOS: Mathematics, Mathematics - Combinatorics, 0307 Theoretical and Computational Chemistry, Pharmacology & Pharmacy, Programming errors, 3404 Medicinal and biomolecular chemistry, 0802 Computation Theory and Mathematics, Science & Technology, Computer Science, Information Systems, CONSTRUCTION, 0304 Medicinal and Biomolecular Chemistry, IPR fullerenes, Computational Physics (physics.comp-ph), Keywords: Cubic planar graphs, Chemistry, CAGE, Physical Sciences, Computer Science, Computer Science, Interdisciplinary Applications, Fullerenes, Combinatorics (math.CO), Life Sciences & Biomedicine, Physics - Computational Physics, Algorithms, 3407 Theoretical and computational chemistry, Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Technology, Discrete Mathematics (cs.DM), Chemistry, Multidisciplinary, Medicinal & Biomolecular Chemistry, FOS: Physical sciences, Chemistry, Medicinal, GRAPHS, FOS: Mathematics, Mathematics - Combinatorics, 0307 Theoretical and Computational Chemistry, Pharmacology & Pharmacy, Programming errors, 3404 Medicinal and biomolecular chemistry, 0802 Computation Theory and Mathematics, Science & Technology, Computer Science, Information Systems, CONSTRUCTION, 0304 Medicinal and Biomolecular Chemistry, IPR fullerenes, Computational Physics (physics.comp-ph), Keywords: Cubic planar graphs, Chemistry, CAGE, Physical Sciences, Computer Science, Computer Science, Interdisciplinary Applications, Fullerenes, Combinatorics (math.CO), Life Sciences & Biomedicine, Physics - Computational Physics, Algorithms, 3407 Theoretical and computational chemistry, Computer Science - Discrete Mathematics
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