扶手椅型纳米管的Graovac-Pisanski指数
The Graovac-Pisanski Index of Armchair Nanotubes
摘要：
Graovac-Pisanski指标，也称为修正的Wiener指标，考虑了分子图的对称性和距离。碳纳米管是由碳制成的具有圆柱形结构的分子，具有不寻常的有价值的特性。在一个数学模型中，我们可以把它们看作是一个嵌入在圆柱上的六边形格子的子图，其中一些顶点是可识别的。本文研究了扶手椅型纳米管的自同构和轨道，导出了其Graovac-Pisanski指数的闭公式。
英文摘要：
The Graovac-Pisanski index, which is also called the modified Wiener index, considers the symmetries and the distances in molecular graphs. Carbon nanotubes are molecules made of carbon with a cylindrical structure possessing unusual valuable properties. In a mathematical model we can consider them as a subgraph of a hexagonal lattice embedded on a cylinder with some vertices being identified. In the present paper, we investigate the automorphisms and the orbits of armchair nanotubes and derive the closed formulas for their Graovac-Pisanski index.
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