Hyperbolic analogues of fullerenes on orientable surfaces (CROSBI ID 182211)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Dutour Sikirić, Mathieu ; Knor, Martin ; Potocnik, Primoz ; Siran, Jozef ; Skrekovski, Riste
engleski
Hyperbolic analogues of fullerenes on orientable surfaces
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.
Fullerene ; Polyhex ; Orientable map ; Cubic map ; Polyhedral map
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Podaci o izdanju
312 (4)
2012.
729-736
objavljeno
0012-365X
1872-681X
10.1016/j.disc.2011.11.009