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

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  • Yang Gao
  • Heping Zhang

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.

Suggested Citation

  • Yang Gao & Heping Zhang, 2014. "Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, August.
    • Handle: RePEc:hin:jnljam:196792
    DOI: 10.1155/2014/196792
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    Cited by:

    1. Shi, Lingjuan & Zhang, Heping, 2019. "Counting Clar structures of (4, 6)-fullerenes," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 559-574.

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