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## Hyperbolic analogues of fullerenes on orientable surfaces

Dutour Sikirić, Mathieu; Knor, Martin; Potocnik, Primoz; Siran, Jozef; Skrekovski, Riste
Hyperbolic analogues of fullerenes on orientable surfaces // Discrete mathematics, 312 (2012), 4; 729-736 doi:10.1016/j.disc.2011.11.009 (međunarodna recenzija, članak, znanstveni)

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Naslov
Hyperbolic analogues of fullerenes on orientable surfaces

Autori
Dutour Sikirić, Mathieu ; Knor, Martin ; Potocnik, Primoz ; Siran, Jozef ; Skrekovski, Riste

Izvornik
Discrete mathematics (0012-365X) 312 (2012), 4; 729-736

Ključne riječi
Fullerene ; Polyhex ; Orientable map ; Cubic map ; Polyhedral map

Sažetak
Mathematical models of fullerenes are cubic spherical maps of type (5, 6), that is, with pentagonal and hexagonal faces only. Any such map necessarily contains exactly 12 pentagons, and it is known that for any integer a>=0 except a=1 there exists a fullerene map with precisely a hexagons. In this paper we consider hyperbolic analogues of fullerenes, modelled by cubic maps of face-type (6, k) for some k>=7 on orientable surface of genus at least two. The number of k- gons in this case depends on the genus but the number of hexagons is again independent of the surface. We focus on the values of k that are universal in the sense that there exist cubic maps of face-type (6, k) for all genera g>=2. By Euler's formula, if k is universal, then k is in {; ; ; ; ; 7, 8, 9, 10, 12, 18}; ; ; ; ; . We show that for any k in {; ; ; ; ; 7, 8, 9, 12, 18}; ; ; ; ; and any g>=2 there exists a cubic map of face-type (6, k) with any prescribed number of hexagons. For k=7 and 8 we also prove the existence of polyhedral cubic maps of face- type (6, k) on surfaces of any prescribed genus g>=2 and with any number of hexagons a, except for the cases k=8, g=2 and a<=2, where we show that no such maps exist.

Izvorni jezik
Engleski

Znanstvena područja
Kemija

Projekti:
098-0982705-2707 - Matematičko modeliranje cirkulacije i satelitska detekcija graničnih procesa (Kuzmić, Milivoj, MZOS ) ( POIROT)

Ustanove:
Institut "Ruđer Bošković", Zagreb

Profili:

Mathieu Dutour Sikirić (autor)

#### Citiraj ovu publikaciju:

Dutour Sikirić, Mathieu; Knor, Martin; Potocnik, Primoz; Siran, Jozef; Skrekovski, Riste
Hyperbolic analogues of fullerenes on orientable surfaces // Discrete mathematics, 312 (2012), 4; 729-736 doi:10.1016/j.disc.2011.11.009 (međunarodna recenzija, članak, znanstveni)
Dutour Sikirić, M., Knor, M., Potocnik, P., Siran, J. & Skrekovski, R. (2012) Hyperbolic analogues of fullerenes on orientable surfaces. Discrete mathematics, 312 (4), 729-736 doi:10.1016/j.disc.2011.11.009.
@article{article, author = {Dutour Sikiri\'{c}, Mathieu and Knor, Martin and Potocnik, Primoz and Siran, Jozef and Skrekovski, Riste}, year = {2012}, pages = {729-736}, DOI = {10.1016/j.disc.2011.11.009}, keywords = {Fullerene, Polyhex, Orientable map, Cubic map, Polyhedral map}, journal = {Discrete mathematics}, doi = {10.1016/j.disc.2011.11.009}, volume = {312}, number = {4}, issn = {0012-365X}, title = {Hyperbolic analogues of fullerenes on orientable surfaces}, keyword = {Fullerene, Polyhex, Orientable map, Cubic map, Polyhedral map} }
@article{article, author = {Dutour Sikiri\'{c}, Mathieu and Knor, Martin and Potocnik, Primoz and Siran, Jozef and Skrekovski, Riste}, year = {2012}, pages = {729-736}, DOI = {10.1016/j.disc.2011.11.009}, keywords = {Fullerene, Polyhex, Orientable map, Cubic map, Polyhedral map}, journal = {Discrete mathematics}, doi = {10.1016/j.disc.2011.11.009}, volume = {312}, number = {4}, issn = {0012-365X}, title = {Hyperbolic analogues of fullerenes on orientable surfaces}, keyword = {Fullerene, Polyhex, Orientable map, Cubic map, Polyhedral map} }

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

• MathSciNet

#### Citati:

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