Graceful and harmonious labellings of trees

  title={Graceful and harmonious labellings of trees},
  author={Robert E. L. Aldred},
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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