User blog comment:Wythagoras/Extension of SCG/@comment-1605058-20130814202444

Using Deedlit's initial sequence you can have:

G1: double loop

G2: double edge

G3: vertex connected to a loop and two edges

G4: vertex connected to a loop and a 3-path

G5: vertex connected to a loop and a 2-path

G6: vertex connected to a loop and an edge

G7: loop

G8: K1,5 with 2 vertices added

etc. I'm too lazy to do analysis