Graphs and Combinatorics

, Volume 6, Issue 4, pp 365–367

On the dimension to represent a graph by a unit distance graph


  • Hiroshi Maehara
    • College of EducationRyukyu University
  • Vojtech Rödl
    • Emory University

DOI: 10.1007/BF01787703

Cite this article as:
Maehara, H. & Rödl, V. Graphs and Combinatorics (1990) 6: 365. doi:10.1007/BF01787703


It is proved that if a graphG has maximum degreed, then its vertices can be represented by distinct unit vectors inR2d so that two vectors are orthogonal if and only if the corresponding vertices are adjacent. As a corollary it follows that if a graph has maximum degreed, then it is isomorphic to a “unit distance graph” inR2d.

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© Springer-Verlag 1990