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.
braced polygon | de Grey graphs | distance graph | Golomb graph | graph dimension | graph embedding | Hadwiger-Nelson problem | Heule graphs | integral embedding | matchstick graph | Mixon graphs | Moser spindle | Parts graphs | tadpole graph | unit-distance embedding | unit neighborhood graph | Voronov-Neopryatnaya-Dergachev graphs | wormald graph
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