Discrete & Computational Geometry

pp 1–4 | Cite as

Unit Distance Graphs and Algebraic Integers

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• Danylo Radchenko

Article

First Online: 18 November 2019

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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 

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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

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

Authors and Affiliations

• Danylo Radchenko
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1. 1.Max Planck Institute for MathematicsBonnGermany