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Graphs and Combinatorics

, Volume 6, Issue 4, pp 365–367 | Cite as

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

  • Hiroshi Maehara
  • Vojtech Rödl
Article

Abstract

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.

Keywords

Unit Vector Unit Distance Distance Graph Distinct Unit Unit Distance Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Lovász, L.: On the Shannon capacity of graphs, IEEE Trans. Inf. Theory Vol. II 25,1, 1–7 (1979)Google Scholar
  2. 2.
    Maehara, H.: On the euclidean dimension of a complete multipartite graph, Discrete Math.72, 285–289 (1988)Google Scholar
  3. 3.
    Maehara, H.: Note on induced subgraphs of the unit distance graphE n, Discrete Comput. Geom.4, 15–18 (1989)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Hiroshi Maehara
    • 1
  • Vojtech Rödl
    • 2
  1. 1.College of EducationRyukyu UniversityOkinawaJapan
  2. 2.Emory UniversityAtlantaUSA

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