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The Graovac-Pisanski index of zig-zag tubulenes and the generalized cut method

机译：The Graovac-Pisanski index of zig-zag tubulenes and the generalized cut method

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摘要

The Graovac-Pisanski index, which is also called the modified Wiener index, was introduced in 1991 by Graovac and Pisanski. This variation of the classical Wiener index takes into account the symmetries of a graph. In 2016 Ghorbani and Klavzar 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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