Geodesic
Disjoint homometric sets in graphs
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 1-4.

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Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h(n) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h. It is shown that (c log n)/(log log n) h(n) n/4, for n > 3.
DOI : 10.26493/1855-3974.174.027
Keywords: Graph distances, homometric subsets, Golumb ruler 
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Michael O. Albertson; Janos Pach; Michael E. Young. Disjoint homometric sets in graphs. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 1-4. doi : 10.26493/1855-3974.174.027. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.174.027/

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