Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces

Yang Gao and Heping Zhang

Journal of Applied Mathematics, 2014, vol. 2014, 1-11

Abstract:

Fowler and Pisanski showed that the Fries number for a fullerene on surface Σ is bounded above by , 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 , where 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 for which Clar numbers attain . We prove that, for a (4,6)-fullerene on surface Σ, its Clar number is bounded above by and its Fries number is bounded above by , 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 for which Clar numbers attain in Hartung’s method.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:196792

DOI: 10.1155/2014/196792

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