Hello, the second graph should have 2 automorphisms, but I see that none of the vertices has exactly the same adjacent vertices, so that I would be able to switch them and form an automorphism. What automorphisms of the second graph are there? Thank you! Also the posted degree of the second graph is incorrect.
There is the identity automorphism, and then the reflection automorphism. The reflection swaps $b$ and $d$. Those are the only two automorphisms.