In an undirected unlabled graph $G=(V,E)$, we want to find a tree as a subgraph, such that the graph can be decomposed into edge disjoint trees(all the tress are isomorphic). How to define such a tree subgraph uniquely? For example, given degree sequence $(1,1)$, we immediately know that it is a path of length $1$.
It is known that every tree is bipartite. Isomorphic bipartite graphs have the same degree sequence. However, the degree sequence does not, in general, uniquely identify a bipartite graph; in some cases, non-isomorphic bipartite graphs may have the same degree sequence. Thus, degree sequence, alone, is not a good definition of such trees.
It is also known that Reconstructing a binary tree uniquely from its preorder and postorder traversals is impossible in general. http://www.cmi.ac.in/~madhavan/courses/programming06/lecture12-21sep2006.txt