Some new results on distance-based graph invariants

We study distance-based graph invariants, such as the Wiener index, the Szeged index, and variants of these two. Relations between the various indices for trees are provided as well as formulas for line graphs and product graphs. This allows us, for instance, to establish formulas for the edge Wiener index of Hamming graphs, C 4 -nanotubes and C 4 -nanotori. We also determine minimum and maximum of certain indices over the set of all graphs with a given number of vertices or edges. Finally, we study the order of magnitude of the edge Wiener and edge Szeged index, responding negatively to a conjecture that is related to the maximization of the edge Szeged index.