# 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…

## 2 Citations

Symmetries in Graceful Trees

- Mathematics
- 2011

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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