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.
K5 = graph flatten for i from 0 to 4 list for j from i+1 to 4 list {i,j}; |
P = onlyPlanar(generateGraphs 5, true) |
areIsomorphic(first P, K5) |
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.