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, issue 1

Abstract: 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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:196792

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