What is the number of automorphisms of a graph with 2n+3 nodes, n distinct edges, and only one triangle?
If $n=3$, there are $3!6!$ automorphisms. If $n=4$, then there are either $2!7!$ (you have nodes with degree 3,2,2,1,0,0,0,0,0,0,0) or $3!2!6!$ (you have nodes with degree 2,2,2,1,1,0,0,0,0,0,0) automorphisms. These are not equal, so I am not sure what the problem is asking.