GRAPH INVARIANTS FOR FULLERENES
GRAPH INVARIANTS FOR FULLERENES
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DOI：
10.1021/ci00025a007
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发表时间：
1995-05-01
期刊：
影响因子：
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通讯作者：
RANDIC, M
中科院分区：
文献类型：
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作者：
BALABAN, AT;LIU, X;RANDIC, M
比较了具有96个碳原子以上的富勒烯（即C-60的所有同分异构体）和具有60-96个碳原子的所有优选的更高的富勒烯（即没有相邻五边形的富勒烯）的几种理论不变量。考虑了四类富勒烯结构：第一类是1812 C-60异构体；第二，他们的双重性；第三种是含有60-96个碳原子的558个隔离五边形富勒烯；第四是他们的双人舞。所研究的不变量要么是纯图理论的（包括几个拓扑指标、哈密顿电路的数量和生成树的数量），要么是与量子化学解释相关的（包括Huckel pi-electron energy和HOMO-LUMO gap）。除了以单个数值（整数、有理数或实数）表示的不变量之外，还探索了几个不变量的关联，例如凯库勒结构的数量与共轭电路的数量。上述一些不变量成功地独特地表征了所研究的富勒烯。这一发现对富勒烯的合理编码和命名具有启示意义。
A comparison is made among several theoretical invariants in characterizing classes of fullerenes with up through 96 carbon atoms, namely all isomers of C-60, and all preferable higher fullerenes (i.e., fullerenes without abutting pentagons) with 60-96 carbon atoms. Four classes of fullerene structures were considered: first, the 1812 C-60 isomers; second, their duals; third, the 558 isolated-pentagon fullerenes with 60-96 carbon atoms; and fourth their duals. The invariants that were investigated are either purely graph-theoretical (including several topological indices, the number of Hamiltonian circuits, and the number of spanning trees), or associated with quantum-chemical interpretations (including Huckel pi-electron energy and HOMO-LUMO gap). In addition to such invariants that are expressed as a single numerical value (integer, rational, or real number), associations of several invariants have also been explored, such as the numbers of Kekule structures with those of conjugated circuits. Some of the above invariants succeeded in uniquely characterizing the studied fullerenes. This finding has implications for a rational coding and nomenclature of fullerenes.