Theorems for carbon cages
Theorems for carbon cages
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DOI：
10.1007/bf01164204
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发表时间：
1992-12
影响因子：
1.7
通讯作者：
D. Klein;X. Liu
中科院分区：
文献类型：
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作者：
D. Klein;X. Liu
为具有三价顶点的笼（或多面体）建立了新的定理。一个定理表明，所有此类笼子都至少具有三个凯库勒结构（或完美匹配）。因此，共振通常是一种可能性。另一个定理说，对于每个偶数顶点数 > 70 的情况，至少有一个“优选”子类的笼子，而对于顶点数 < 70 的唯一优选笼子是截角二十面体的笼子。因此，巴克敏斯特富勒烯结构对于 C60 的独特作用在数学上得到了体现。[/p]
New theorems are established for cages (or polyhedra) with trivalent vertices. One theorem says that all such cages have at least three Kekulé structures (or perfect matchings). Thence, resonance generally appears as a possibility. Another theorem says that for every even vertex count >70 there is at least one cage of a “preferable” subclass, while for vertex count <70 the sole preferable cage is that of the truncated icosahedron. Thence, the unique role of the buckminsterfullerene structure for C60is mathematically indicated.[/p]