Abstract
We answer a question of Brass about vertex degrees in unit distance graphs of finitely generated additive subgroups of \(\mathbb {R}^2\).
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References
Brass, P.: Erdős distance problems in normed spaces. Comput. Geom. 6(4), 195–214 (1996)
Brass, P., Moser, W., Pach, J.: Research Problems in Discrete Geometry. Springer, Berlin (2005)
Erdős, P.: On sets of distances of \(n\) points. Am. Math. Mon. 53, 248–250 (1946)
Salem, R.: Algebraic Numbers and Fourier Analysis. D. C. Heath and Co., Boston (1963)
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Radchenko, D. Unit Distance Graphs and Algebraic Integers. Discrete Comput Geom 66, 269–272 (2021). https://doi.org/10.1007/s00454-019-00152-4
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DOI: https://doi.org/10.1007/s00454-019-00152-4