On 0-rotatable trees

For a tree T on n vertices, if it admits a mapping f : V(T){0,1,...,n-1} such that f(x)f(y) for distinct x, y V(T) and an edge uv has its label as f(uv)=|f(u)-f(v)|, and the set {f(uv)|uv E(T)}={1,2,...,n-1}, then we say T is a graceful tree and f a graceful labeling of T. Furthermore, if for any vertex u V(T), T admits a graceful labeling f such that f(u)=0, then we say T to be a 0-rotatable tree. Some constructive methods for building large scale of 0-rotatable trees are given.