I'm looking for an undirected graph $G$ which contains as induced subgraphs:
- the six $4$-node connected graphs and,
- the twenty one $5$-node connected graphs.
Ideally, I would also like it to be as small as possible (least number of nodes). If we take the union of these graphs, it has $6 \times 4+21 \times 5=129$ nodes. If we take the graphs and identify them at a point, it has $6 \times 4+21 \times 5-(6+21)+1=103$ nodes.
This would be helpful for testing our program for network motif detection program (NetMODE), which searches for connected induced subgraphs in networks.
If it helps, I've attached a picture of the graphs below: