The Wiener Index and the Szeged Index of Benzenoid Systems in Linear Time

A linear time algorithm is presented which, for a given benzenoid system G, computes the Wiener index of G. The algorithm is based on an isometric embedding of G into the Cartesian product of three trees, combined with the notion of the Wiener index of vertex-weighted graphs. An analogous approach yields also a linear algorithm for computing the Szeged index of benzenoid systems.

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