• Corpus ID: 5998052

A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree

@article{Gilbert2007ACP,
  title={A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree},
  author={Jesse Gilbert},
  journal={ArXiv},
  year={2007},
  volume={abs/0709.2201}
}
The Graceful Tree Conjecture claims that every finite simple tree of order n can be vertex labeled with integers {1, 2, ...n} so that the absolute values of the differences of the vertex labels of the end-vertices of edges are all distinct. That is, a graceful labeling of a tree is a vertex labeling f , a bijection f : V (Tn) −→ {1, 2, ...n}, that induces an edge labeling g(uv) = |f(u) − f(v)| that has a special property g : E(G) −→ {1, 2, ..n − 1} is a bijection. The Graceful Tree Conjecture… 
Symmetries in Graceful Trees
We study how to exploit symmetries in the context of the famou s graceful tree conjecture. Current work on graceful labelli ng of graphs focused on breaking the value symmetry and the structural

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