A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. The Fáry theorem established that every planar graph has a planar straight line embedding with noncrossing edges, and such embeddings (with rectilinear crossing number 0) are sometimes known as a Fáry embedding. A planar straight line embedding of a planar graph can be constructed in the Wolfram Language using the PlanarEmbedding option to GraphLayout or in the Wolfram Language using PlanarGraph[g]. de Fraysseix et al. (1988) give an algorithm for constructing a planar straight line embedding for a planar graph of order n by placing the vertices on a (2n - 4)×(n - 2) grid.
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