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Sharp Upper Bounds on the Clar Number of Fullerene Graphs

Yang Gao;  Heping Zhang — 2018

Discussiones Mathematicae Graph Theory

The Clar number of a fullerene graph with n vertices is bounded above by ⌊n/6⌋ − 2 and this bound has been improved to ⌊n/6⌋ − 3 when n is congruent to 2 modulo 6. We can construct at least one fullerene graph attaining the upper bounds for every even number of vertices n ≥ 20 except n = 22 and n = 30.

Stabilities of F-Yang-Mills fields on submanifolds

Gao-Yang Jia;  Zhen Rong Zhou — 2013

Archivum Mathematicum

In this paper, we define an F -Yang-Mills functional, and hence F -Yang-Mills fields. The first and the second variational formulas are calculated, and the stabilities of F -Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investigated, and hence the theories of Yang-Mills fields are generalized in this paper.

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