# Math Help - Graph isomorphism...example help please

1. ## Graph isomorphism...example help please

Is there a graph with exactly 3 components, exactly 2 of them not isomorphic? If so, give the example. If not, explain.

Please help.

2. Originally Posted by zhupolongjoe
Is there a graph with exactly 3 components, exactly 2 of them not isomorphic? If so, give the example. If not, explain.
Think about it a moment. $\binom{3}{2}=3$.
So there are 3 distinct pairs.
Can exactly two components be non-isomorphic?

3. Hmm...No it is not. Because if A and B are the exactly two non-isomorphic graphs, then C must be isomorphic to something, but if it is isomorphic to A, there is only one nonisomorphic component. A contradiction.

Is it that simple?