An Equivalent of Graceful Tree Conjecture

This thesis have mainly discussed a tree is graceful if and only if its subdivision admits an almost-strongly graceful labelling,i.e., an equivalent of Graceful Tree Conjecture. We have done to the correctness of our algorithms by Procedure towards the zero-label, but we do not go to the computer implementation of these algorithms. Two examples show that the application value of equivalence of graceful tree is malleable.