On the connectivity of unit distance graphs
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For a number field K ⊆ ℝ, consider the graph G(Kd), whose vertices are elements of Kd, with an edge between any two points at (Euclidean) distance 1. We show that G(K2) is not connected whileG(Kd) is connected ford ≥ 5. We also give necessary and sufficient conditions for the connectedness of G(K3) and G(K4).
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