锯齿形管状分子的Graovac-Pisanski指数和广义割方法
The Graovac-Pisanski Index of Zig-Zag Tubulenes and the Generalized Cut Method
摘要：
Graovac-Pisanski指数，又称修正的Wiener指数，是由A. Graovac和T.皮桑斯基经典维纳指数的这种变化考虑了图的对称性。2016年M. Ghorbani和S. Klavžar使用本文中推广的切割方法计算了该指数。此外，我们还证明了在某些情况下，锯齿形管状分子的自同构群同构于二面体群与循环群的直积。最后，计算了锯齿形管的Graovac-Pisanski指数的闭公式。
英文摘要：
The Graovac-Pisanski index, which is also called the modified Wiener index, was introduced in 1991 by A. Graovac and T. Pisanski. This variation of the classical Wiener index takes into account the symmetries of a graph. In 2016 M. Ghorbani and S. Klavžar calculated this index by using the cut method, which we generalize in this paper. Moreover, we prove that in some cases the automorphism group of a zig-zag tubulene is isomorphic to the direct product of a dihedral group and a cyclic group. Finally, the closed formulas for the Graovac-Pisanski index of zig-zag tubulenes are calculated.
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