Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces
نویسندگان
چکیده
منابع مشابه
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 α ≥ 0 except α = 1 there exists a fullerene map with precisely α hexagons. In this paper we consider hyperbolic analogues of fullerenes, modelled by cubic maps of face-type (6, k...
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Mathematical models of fullerenes are cubic planar maps with pentagonal and hexagonal faces. As a consequence of Eulers’s formula the number of pentagons in such a map is 12. Conversly, for any integer α ≥ 0, there exists a fullerene map with precisely α hexagons unless α = 1. In this paper, we consider hyperbolic analogues of fullerenes, which are defined as cubic maps of face-type (6, k) on o...
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If a fullerene is defined as a finite trivalent graph made up solely of pentagons and hexagons, embedding in only four surfaces is possible: the sphere, torus, Klein bottle, and projective (elliptic) plane. The usual spherical fullerenes have 12 pentagons; elliptic fullerenes, 6; and toroidal and Klein-bottle fullerenes, none. Klein-bottle and elliptic fullerenes are the antipodal quotients of ...
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Both the eigenfunctions and the local density of states (DOS) near the pentagonal defects on the fullerenes was calculated analytically as a numerically. The results shows that the low-energy DOS has a cusp which drops to zero at the Fermi energy for any number of pentagons at the tip except three. For three pentagons, the nonzero DOS across the Fermi level is formed. Graphite is an example of ...
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The recent interest in using Buckminsterfullerene (fullerene) derivatives in biological systems raises the possibility of their assay by immunological procedures. This, in turn, leads to the question of the ability of these unprecedented polygonal structures, made up solely of carbon atoms, to induce the production of specific antibodies. Immunization of mice with a C60 fullerene derivative con...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/196792