The problem of labelling the complete graph K,, as near to graceful as possible is equivalent to the 'Golomb ruler problem' of finding as short a ruler as possible with n integer marks such that the distances between pairs of marks are all distinct. We generalize this to an association between label
โฆ LIBER โฆ
Distinct Distances in Homogeneous Sets in Euclidean Space
โ Scribed by Jozsef Solymosi; Csaba D. Toth
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 230 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0179-5376
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A distinct distance set (DD set) for a graph G is a vertex subset of G with the property that for ISI = s, we have (~) distinct distances of the pairs of vertices in S. In this article, it is shown that (a) For 6 ~< k ~< 18 there exists a tree T with DD(T) = k and din(T) = LB(k) < B~(Kk). where LB(