Modified Wiener index via canonical metric representation, and some fullerene patches - Ghorbani, Modjtaba (Ars mathematica contemporanea, 2016)
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.
Keywords: canonical metric representation; delne kocke; fulerenske krpanke; fullerene patches; kanonična metrična reprezentacija; modificirani Wienerjev index; modified Wiener index; nanocevke; nanocones; partial cubes