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

Relationship Between the Hosoya Polynomial and the Edge-Hosoya Polynomial of Trees