(New page: Isn't this trivial? If G and H have the same shape, then their complements must have the same shape... I don't know a way to "show" it. --~~~~) |
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Isn't this trivial? If G and H have the same shape, then their complements must have the same shape... I don't know a way to "show" it. --[[User:Mkorb|Mkorb]] 18:33, 12 November 2008 (UTC) | Isn't this trivial? If G and H have the same shape, then their complements must have the same shape... I don't know a way to "show" it. --[[User:Mkorb|Mkorb]] 18:33, 12 November 2008 (UTC) | ||
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| + | I think you need to actually construct a function that produces an isomorphism between the complement of G and the complement of H. Consider the function that does the "opposite" of the function that assigns the isomorphism from G to H. | ||
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| + | Consider how to describe the complement of a graph in terms of G, H and their respective complete graphs. Then show that they are isomorphic. | ||
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| + | --[[User:ysuo|ysuo]] | ||
Latest revision as of 11:40, 14 November 2008
Isn't this trivial? If G and H have the same shape, then their complements must have the same shape... I don't know a way to "show" it. --Mkorb 18:33, 12 November 2008 (UTC)
I think you need to actually construct a function that produces an isomorphism between the complement of G and the complement of H. Consider the function that does the "opposite" of the function that assigns the isomorphism from G to H.
Consider how to describe the complement of a graph in terms of G, H and their respective complete graphs. Then show that they are isomorphic.
--ysuo
