Computing distance moments on graphs with transitive Djoković-Winkler relation

The cut method proved to be utmost useful to obtain fast algorithms and closed formulas for classical distance based invariants of graphs isometrically embeddable into hypercubes. These graphs are known as partial cubes and in particular contain numerous chemically important graphs such as trees, benzenoid graphs, and phenylenes. It is proved that the cut method can be used to compute an arbitrary distance moment of all the graphs that are isometrically embeddable into Cartesian products of triangles, a class much larger than partial cubes. The method in particular covers the Wiener index, the hyper-Wiener index, and the Tratch-Stankevich-Zefirov index.