Abstract: A tree of order n is
said to be graceful if the vertices can be assigned the labels
{0,1,2,...,n-1} such that the absolute value of the differences in vertex
labels between adjacent vertices generate the set {1,2,...,n-1}. The
Graceful Tree Conjecture is the unproven claim that all trees are graceful. We present
major results known on graceful trees from those dating from the problem's
origin to recent developments. Constructions and classes of graceful
trees are
given as well as an analysis of various lines of attack on the
Conjecture. We also examine other types of graph
labellings
as they relate to the Conjecture.