Another Gracefull Trees
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    Abstract:

    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…vnsuch 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.

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History
  • Received:July 08,2007
  • Revised:
  • Adopted:
  • Online: December 07,2012
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