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A generation algorithm for nanojoins

Gunnar Brinkmann (UGent) and Dieter Mourisse (UGent)
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Abstract
Nanojoins or nanojunctions are substructures of large Carbon molecules that connect two or more nanotubes with the same or different tube parameters. Except in the trivial case where two tubes with the same parameters are connected, nanojoins also contain one or more heptagons in addition to hexagons and possibly pentagons like they also occur in fullerenes and nanotubes. We consider nanojoins as isomorphic when the infinite molecules given by the join connected to infinite tubes are isomorphic. Even when fixing the number of tubes to be connected, the tube parameters, and the number of pentagons and heptagons, there are in most cases infinitely many non-isomorphic nanojoins, so complete enumeration is impossible unless also a parameter restricting the size of the join is added. In this article we describe an algorithm for complete enumeration of non-isomorphic nanojoins for a given set of tube parameters, number of heptagons, and an upper bound on the number of faces in the join. We also give performance statistics and results for some parameter sets.
Keywords
Nanotube, Fullerene, Nanojoin, CONSTRUCTIVE ENUMERATION, CARBON NANOTUBES, FULLERENES, JUNCTIONS

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Citation

Please use this url to cite or link to this publication:

Chicago
Brinkmann, Gunnar, and Dieter Mourisse. 2017. “A Generation Algorithm for Nanojoins.” Match-communications in Mathematical and in Computer Chemistry 78 (3): 713–736.
APA
Brinkmann, G., & Mourisse, D. (2017). A generation algorithm for nanojoins. MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 78(3), 713–736.
Vancouver
1.
Brinkmann G, Mourisse D. A generation algorithm for nanojoins. MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY. 2017;78(3):713–36.
MLA
Brinkmann, Gunnar, and Dieter Mourisse. “A Generation Algorithm for Nanojoins.” MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY 78.3 (2017): 713–736. Print.
@article{8545502,
  abstract     = {Nanojoins or nanojunctions are substructures of large Carbon molecules that connect two or more nanotubes with the same or different tube parameters. Except in the trivial case where two tubes with the same parameters are connected, nanojoins also contain one or more heptagons in addition to hexagons and possibly pentagons like they also occur in fullerenes and nanotubes. 
We consider nanojoins as isomorphic when the infinite molecules given by the join connected to infinite tubes are isomorphic. Even when fixing the number of tubes to be connected, the tube parameters, and the number of pentagons and heptagons, there are in most cases infinitely many non-isomorphic nanojoins, so complete enumeration is impossible unless also a parameter restricting the size of the join is added. In this article we describe an algorithm for complete enumeration of non-isomorphic nanojoins for a given set of tube parameters, number of heptagons, and an upper bound on the number of faces in the join. We also give performance statistics and results for some parameter sets.},
  author       = {Brinkmann, Gunnar and Mourisse, Dieter},
  issn         = {0340-6253},
  journal      = {MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY},
  keywords     = {Nanotube,Fullerene,Nanojoin,CONSTRUCTIVE ENUMERATION,CARBON NANOTUBES,FULLERENES,JUNCTIONS},
  language     = {eng},
  number       = {3},
  pages        = {713--736},
  title        = {A generation algorithm for nanojoins},
  url          = {http://match.pmf.kg.ac.rs/electronic_versions/Match78/n3/match78n3_713-736.pdf},
  volume       = {78},
  year         = {2017},
}

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