On the connectedness of some geometric graphs

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Fos S ⊆ R, let G(Sd) denote the graph, obtained from all the points of the real d-space Rd having their coordinates in S, by connecting every two points which are at distance one. If S = Q (the rationals), or Q[√k], or Q[a] where a is a real algebraic number, then G(Sd) is shown to be connected for all large values of d. Similar results are obtained in the case of S = Q[n k], where the distance is computed in the lp-norm, p an integer, p ≥ 3 and n∥p (or n = 2).

Original languageEnglish
Pages (from-to)143-150
Number of pages8
JournalJournal of Combinatorial Theory. Series B
Issue number2
StatePublished - Aug 1990

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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