How to prove these graphs are isomorphic or not?

Question

Using human intuition I think the graphs are not isomorphic because the loops are on opposite sides but I do not have a formal proof for it. I ran the basic checks and I still cant disprove it.

1. Check if vertex set cardinalities differ - 5 for both
2. Check if edge set cardinalities differ - 8 for both
3. Compare degree sequences - (4,3,3,3,2) for both
4. Compare number of connected components - 1 for both
5. Compare cycle lengths - 3 and 4 for both

What other conditions can I use to disprove graph isomorphism?

EDIT: Can I use the sequence of degrees of vertices in cycles?

Answer 1

I would say that in both there are exactly two vertices with valency $4$. The two are adjacent in one graph, but not in the other.