On Reconstructing Rooted Trees

A probably very difficult question of Nash-Williams asks whether any two hypomorphic trees are isomorphic. In the present paper, we consider rooted trees rather than trees and give an affirmative answer to the corresponding version of Nash-Williams′ question, i.e., we show that any two hypomorphic rooted trees are isomorphic. Further related results are given, together with applications to the reconstruction of unrooted trees.