Checking if these two are graph isomorphisms I know a few graph invariants and it seemed that these two graphs do not have the same amount of circuit length $3$. (our definition of a circuit is a closed path, a path being a walk with no repeated edges) . $G_2$ has only $6$ circuits of length $3$ in the anti-clockwise direction so it has $12$ circuits in total of length $3$. So $G_1$ is not isomorphic to $G_2$, however, my solutions say that they are.

Actually these graphs are isomorphic. If you take f(a)=z f(b)=u f(e)=t f(d)=x f(c)=y f is an isomorphism because if ab is an edge in G1, f(a)f(b) is an edge in G2