I have the following graphs and I am trying to identify if they are isomorphic or not.
The solutions that I have indicate they are isomorphic, with the following bijection:
However, it appears that the graph on the right has more 3-cycles than the graph on the left. The graph on the left also contains an obvious 4-cycle, where the graph on the right does not. The degrees of all the vertices are the same.
It's my understanding that two graphs cannot be isomorphic if they have a differing number of x-cycles. What am I missing here?