Another Gracefull Trees
Zheng Xie · Journal of National University of Defense Technology · 2008
In 1966,Rosa conjectured that all trees are graceful,which has ever since been considered the famous Graceful Tree Conjecture(GTC).Now the conjecture still remains to be an open problem,and only a few kinds of trees are proved to be graceful.The number,however,can be enlarged by the approach presented in the paper.For any integer k∈{0,1,2,…,n} and 4k≠n,3n,there exists a bipartited labeling f of path Pn=v0v1…vn such that f(v0)=k.Based on this,a method for constructing bigger graceful trees by joining a path to a graceful tree is given and this makes much more trees to be graceful.