Graceful and harmonious labellings of trees

@inproceedings{Aldred2007GracefulAH,
  title={Graceful and harmonious labellings of trees},
  author={Robert E. L. Aldred},
  year={2007}
}
We establish that all trees on at most 27 vertices admit graceful labellings and all trees on at most 26 vertices admit harmonious labellings. A graceful labelling of a graph G with q edges is an injection f : V (G) → {0, 1, 2, . . . , q} such that when each edge xy ∈ E(G) is assigned the label, |f(x) − f(y)|, all of the edge labels are distinct. A graph which admits a graceful labelling is said to be graceful. This idea was introduced by Rosa [5] where it was shown that if all trees are… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-6 of 6 references

Status of the graceful tree conjecture in 1989, in Topics in Cominatorics and Graph Theory, R

  • I. Cahit
  • Bodendiek and R. Henn (eds), Physica-Verlag…
  • 1990
1 Excerpt

On certain valuations of the vertices of a graph, in Theory of Graphs (Internat

  • A. Rosa
  • 1966
2 Excerpts

Problem 25, in Theory of Graphs and its Applications

  • G. Ringel
  • Proc. Symposium SSmolenice 1963,
  • 1963
1 Excerpt

Status of the graceful tree conjecture in 1989

  • R. Henn

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