Pairwise non-isomorphic formality

Hey everyone, I am trying to solve a problem which is:

Find the number of pairwise non-isomorphic graphs with a certain property (the property is not important).

My problem is that I have shown that all graphs with this given property are isomorphic, but now I am unsure as to whether this means there are NO pairwise non-isomorphic graphs of this type, since any 2 graphs you choose will be isomorphic (so the answer is 0), or whether since they are all isomorphic, we have a single isomorphism class and the answer is 1 (since we consider all graphs to be 'the same')

It's an annoying formality, but I can't get my head around it. (Headbang)

Any help on the matter would be much appreciated. Thanks.