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On the connectivity of unit distance graphs

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Abstract

For a number field K ⊆ ℝ, consider the graph G(K d), whose vertices are elements of K d, with an edge between any two points at (Euclidean) distance 1. We show that G(K 2) is not connected whileG(K d) is connected ford ≥ 5. We also give necessary and sufficient conditions for the connectedness of G(K 3) and G(K 4).

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  1. Michael Reid

    Present address: , Three Oak Terrace #6, 02143, Somerville, MA, USA

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  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Michael Reid

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  1. Michael Reid
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Reid, M. On the connectivity of unit distance graphs. Graphs and Combinatorics 12, 295–303 (1996). https://doi.org/10.1007/BF01858462

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  • DOI: https://doi.org/10.1007/BF01858462

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