My reasoning was that they were isomorphisms because you could just flip the bottom two nodes and you would have the same graph. They should be eligible to be isomorphisms because they have the same number of nodes, vertices, and degrees. The answer key says they are not isomorphic but provides no reasoning. Could anyone shed some light on this?
Graph $Y$ has a vertex ($6$) of degree $2$ whose neighbours are not connected to each other.
Graph $X$ has no such vertex.