Advertisement

Unit Distance Graphs and Algebraic Integers

  • Danylo RadchenkoEmail author
Article
  • 12 Downloads

Abstract

We answer a question of Brass about vertex degrees in unit distance graphs of finitely generated additive subgroups of \(\mathbb {R}^2\).

Keywords

Discrete geometry Unit distance graphs Salem numbers 

Mathematics Subject Classification

52C10 11R06 

Notes

References

  1. 1.
    Brass, P.: Erdős distance problems in normed spaces. Comput. Geom. 6(4), 195–214 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brass, P., Moser, W., Pach, J.: Research Problems in Discrete Geometry. Springer, Berlin (2005)zbMATHGoogle Scholar
  3. 3.
    Erdős, P.: On sets of distances of \(n\) points. Am. Math. Mon. 53, 248–250 (1946)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Salem, R.: Algebraic Numbers and Fourier Analysis. D. C. Heath and Co., Boston (1963)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Max Planck Institute for MathematicsBonnGermany

Personalised recommendations