A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of length 1. It is therefore a special case of an integral embedding. By their definition, unit-distance graphs have graph dimension of 2 or less (with 0 and 1 corresponding to the trivial connected cases of the singleton graph K_1 and path graph P_n, respectively). The smallest value of d for which a graph is unit distance is called its graph dimension.

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