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Euler Graph Generator. Given the number of nodes in the desired graph. Tour start_vertex graph00 tourappendstart_vertex while lengraph 0.
If it gives you problems let me know. A graph is called Eulerian if it has an Eulerian Cycle and called Semi-Eulerian if it has an Eulerian Path. Followings are some of these templates.
A connected graph G is an Euler graph if and only if all vertices of G are of even degree and a connected graph G is Eulerian if and only if its edge set can be decomposed into cycles.
OEIS A133736 the first few of which are illustrated above. Another approach for generating Euler diagrams with circles Stapleton et al. Euler Diagram Number Sets Example. Followings are some of these templates.