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.
Citation
Yang Gao. Heping Zhang. "Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces." J. Appl. Math. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/196792
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