A graph is planar if the graph can be embedded in the plane, i.e., the vertices can be arranged such that no edges cross except at vertices.
The only non-planar graph on five vertices is the complete graph.
i1 : K5 = graph flatten for i from 0 to 4 list for j from i+1 to 4 list {i,j};
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i2 : P = onlyPlanar(generateGraphs 5, true)
o2 = {D~{}
o2 : List
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i3 : areIsomorphic(first P, K5)
o3 = true
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This method uses the program planarg. The code was written by Paulette Lieby for the Magma project and used with permission in the software nauty.