Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces
Fowler and Pisanski showed that the Fries number for a fullerene on surface Σ is bounded above by |V|/3, and fullerenes which attain this bound are exactly the class of leapfrog fullerenes on surface Σ. We showed that the Clar number of a fullerene on surface Σ is bounded above by (|V|/6)-χ(Σ), wher...
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2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/196792 |
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| author | Yang Gao Heping Zhang |
| author_facet | Yang Gao Heping Zhang |
| author_sort | Yang Gao |
| collection | DOAJ |
| description | Fowler and Pisanski showed that the Fries number for a fullerene on surface Σ is bounded above by |V|/3, and fullerenes which attain this bound are exactly the class of leapfrog fullerenes on surface Σ. We showed that the Clar number of a fullerene on surface Σ is bounded above by (|V|/6)-χ(Σ), where χ(Σ) stands for the Euler characteristic of Σ. By establishing a relation between the extremal fullerenes and the extremal (4,6)-fullerenes on the sphere, Hartung characterized the fullerenes on the sphere S0 for which Clar numbers attain (|V|/6)-χ(S0). We prove that, for a (4,6)-fullerene on surface Σ, its Clar number is bounded above by (|V|/6)+χ(Σ) and its Fries number is bounded above by (|V|/3)+χ(Σ), and we characterize the (4,6)-fullerenes on surface Σ attaining these two bounds in terms of perfect Clar structure. Moreover, we characterize the fullerenes on the projective plane N1 for which Clar numbers attain (|V|/6)-χ(N1) in Hartung’s method. |
| format | Article |
| id | doaj-art-709ae3b3950a4fceb6460986d062b54c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-709ae3b3950a4fceb6460986d062b54c2025-02-03T06:08:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/196792196792Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on SurfacesYang Gao0Heping Zhang1School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaFowler and Pisanski showed that the Fries number for a fullerene on surface Σ is bounded above by |V|/3, and fullerenes which attain this bound are exactly the class of leapfrog fullerenes on surface Σ. We showed that the Clar number of a fullerene on surface Σ is bounded above by (|V|/6)-χ(Σ), where χ(Σ) stands for the Euler characteristic of Σ. By establishing a relation between the extremal fullerenes and the extremal (4,6)-fullerenes on the sphere, Hartung characterized the fullerenes on the sphere S0 for which Clar numbers attain (|V|/6)-χ(S0). We prove that, for a (4,6)-fullerene on surface Σ, its Clar number is bounded above by (|V|/6)+χ(Σ) and its Fries number is bounded above by (|V|/3)+χ(Σ), and we characterize the (4,6)-fullerenes on surface Σ attaining these two bounds in terms of perfect Clar structure. Moreover, we characterize the fullerenes on the projective plane N1 for which Clar numbers attain (|V|/6)-χ(N1) in Hartung’s method.http://dx.doi.org/10.1155/2014/196792 |
| spellingShingle | Yang Gao Heping Zhang Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces Journal of Applied Mathematics |
| title | Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces |
| title_full | Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces |
| title_fullStr | Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces |
| title_full_unstemmed | Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces |
| title_short | Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces |
| title_sort | clar structure and fries set of fullerenes and 4 6 fullerenes on surfaces |
| url | http://dx.doi.org/10.1155/2014/196792 |
| work_keys_str_mv | AT yanggao clarstructureandfriessetoffullerenesand46fullerenesonsurfaces AT hepingzhang clarstructureandfriessetoffullerenesand46fullerenesonsurfaces |