  We prove the relationship between the Hosoya polynomial and the edge-Hosoya
polynomial of trees. The connection between the edge-hyper-Wiener index and the
edge-Hosoya polynomial is established. With these results we also prove
formulas for the computation of the edge-Wiener index and the edge-hyper-Wiener
index of trees using the Wiener index and the hyper-Wiener index. Moreover, the
closed formulas are derived for a family of chemical trees called regular
dendrimers.
