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A variation of the classical Wiener index, the modified Wiener index, that was introduced in 1991 by Graovac and Pisanski , takes into account the symmetries of a given graph. In this paper it is proved that the computation of the modified Wiener index of a graph G  can be reduced to the computation of the Wiener indices of the appropriately weighted quotient graphs of the canonical metric representation of G . The computation simplifies in the case when G  is a partial cube. The method developed is applied to two infinite families of fullerene patches.

Modified Wiener index via canonical metric representation, and some fullerene patches