I'm supposed to determine if the above graphs are isomorphic. I thought there was because there was a bijection from the set of vertices of graph G to the set of vertices of graph H, and because adjacency as preserved. However, this was my book's explanation as to why it was NOT isomorphic:
I understand that since a has a degree of 2, it can only correspond to either t, u, x, or y. However, I don't understand why the fact that those vertices in H are adjacent to other vertices of degree two makes the graphs not isomorphic. The book didn't say anything further than that, so I guess it should be self-evident and obvious, but I really don't understand what that has to do with anything. Can somebody explain this?