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