Is there a graph with exactly 3 components, exactly 2 of them not isomorphic? If so, give the example. If not, explain. Please help.
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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. $\displaystyle \binom{3}{2}=3$. So there are 3 distinct pairs. Can exactly two components be non-isomorphic?
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?
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