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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.
In this paper, we define an -Yang-Mills functional, and hence -Yang-Mills fields. The first and the second variational formulas are calculated, and the stabilities of -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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