Graphs and Combinatorics

, Volume 4, Issue 1, pp 23–30

On the euclidean dimension of a wheel

  • Fred Buckley
  • Frank Harary
Article

Abstract

Following Erdös, Harary, and Tutte, the euclidean dimension of a graphG is the minimumn such thatG can be embedded in euclideann-spaceRn so that each edge ofG has length 1. We present constructive proofs which give the euclidean dimension of a wheel and of a complete tripartite graph. We also define the generalized wheelWm,n as the join\(\bar K_m + C_n \) and determine the euclidean dimension of all generalized wheels.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Erdös, P.: On sets of distances ofn points in Euclidean space. Publ. Math. Inst. Hungar. Acad. Sci.5, 165–169 (1960)Google Scholar
  2. 2.
    Erdös, P., Harary, F., Tutte, W.T.: On the dimension of a graph. Mathematika12, 118–122 (1965)Google Scholar
  3. 3.
    Harary, F.: Graph Theory. Reading: Addison-Wesley 1969Google Scholar
  4. 4.
    Harary, F., Melter, R.: The graphs with no equilateral triangles. Gaz. Mat., Bucur.3, 182–183 (1982)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Fred Buckley
    • 1
  • Frank Harary
    • 2
  1. 1.Baruch College (CUNY)New YorkUSA
  2. 2.New Mexico State UniversityLas CrucesUSA

Personalised recommendations