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

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.

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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

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131396
Digital Object Identifier: 10.1155/2014/196792

Rights: Copyright © 2014 Hindawi

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