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 : R = QQ[a..e];
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i2 : K5 = completeGraph R;
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i3 : P = onlyPlanar(generateGraphs 5, true)
o3 = {D~{}
o3 : List
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i4 : areIsomorphic(first P, K5)
o4 = 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.