Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-05
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Gao, Yang& Zhang, Heping. 2014. Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-453731
Modern Language Association (MLA)
Gao, Yang& Zhang, Heping. Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces. Journal of Applied Mathematics No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-453731
American Medical Association (AMA)
Gao, Yang& Zhang, Heping. Clar Structure and Fries Set of Fullerenes and (4,6)-Fullerenes on Surfaces. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-453731
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-453731