A unit-distance graph is a distance graph having a straight line embedding in the Euclidean plane (i.e., a planar straight line embedding) in which vertices are distinct points and all edges are of length 1. Such an embedding is called a unit-distance embedding and is a special case of an integral embedding. By their definition, unit-distance graphs have graph dimension of d = 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 dimension d for which a graph G has a unit-distance embedding in Euclidean space R^d is called the graph dimension of G.

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