Work so far (please correct if wrong): I think none of them are isomorphic to each other except for maybe the bottom two.
My real question is: What kind of group would the last one (the solid hexagon) represent? My book says that an undirected edge means that the generator associated with that edge is its own inverse. But since there only seems to be one generator on that graph (i.e. one kind of edge), if that generator is its own inverse, shouldn't there only be two distinct points on the diagram rather than six? (the two elements being the generator and the identity element?)
[Edit: Taking David's answer into account, it looks like the last one and the second one from the top are isomorphic to each other (since they are both isomorphic to $\mathbb{Z}_6$). Problem resolved]