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06/21/2011 06:59:40 AM · #6876 |
| i feel exorcised and reposessed |
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06/21/2011 07:05:08 AM · #6877 |
| it's a new day. ...dammit! I forgot to do that thing you're supposed to do at nighttime! |
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06/21/2011 07:47:23 AM · #6878 |
| You are the weakest link... Goodbye! |
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06/21/2011 08:18:04 AM · #6879 |
| Meh, I need to go get a couple hours sleep anywho. |
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06/21/2011 11:58:46 AM · #6880 |
| :::fills art's hand with shaving cream while he sleeps::: |
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06/21/2011 12:26:34 PM · #6881 |
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06/21/2011 01:23:37 PM · #6882 |
| Let him sleep...let him sleep! |
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06/21/2011 04:05:37 PM · #6883 |
Let G be a graph and G' its complement. Further, let A(G) be the automorphism group of G, and A(G') that of G'. Then A(G) is isomorphic to A(G').
Proof: If deg(G) = 1, the proof is obvious, and we assume deg(G) >= 2. It suffices to show that the automorphisms of G and G' are the same. Let a be an automorphism of G, and suppose a is not an automorphism of G'. Then there are two vertices, u, v of G, such that the following statements are true:
- (u, v) and (a(u), a(v)) have the same adjacency in G (i.e. both or neither are edges)
- (u, v) in G has different adjacency than (u, v) in G' (definition of graph complement)
- (u, v) and (a(u), a(v)) have different adjacency in G' (a is not an automorphism of G')
This implies that (a(u), a(v)) have the same adjacency in both G and G'. This is clearly a contradiction, since G and G' are complementary graphs and can't have any edges in common. A similar argument shows that the automorphisms of G' are the same as those of G. The proof is complete.
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06/21/2011 04:35:48 PM · #6884 |
| damn. I can't decide if anthropomorhisms are good, bad, or just plain inedible. |
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06/21/2011 05:32:45 PM · #6885 |
Originally posted by tnun:
damn. I can't decide if anthropomorhisms are good, bad, or just plain inedible. |
Martha Stewart told me you can make very nice gift baskets out of them. ...and that's a good thing.
She also called to congratulate me on my win. That's also a good thing. |
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06/21/2011 06:46:16 PM · #6886 |
| morhersms, anthropomorhersms. martha, schmartha. |
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06/21/2011 10:33:40 PM · #6887 |
| mumble, mumble, mumble.... |
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06/21/2011 10:34:26 PM · #6888 |
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06/21/2011 10:42:15 PM · #6889 |
Yes, I DID say that...haaaahahaha!
ZAP!
 now, be nice! :P |
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06/22/2011 01:19:15 AM · #6890 |
PFTZPPPPZZZZZ
Malfunction. Something has gone terribly wrong. Everyone please be completely silent while I figure this out. |
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06/22/2011 05:47:43 AM · #6891 |
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06/22/2011 06:58:12 AM · #6892 |
| hey im not a bad looking girl. might have to do something about the goatee though |
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06/22/2011 10:52:52 AM · #6893 |
You all need to leave or else.... |
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06/22/2011 10:56:05 AM · #6894 |
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06/22/2011 11:05:03 AM · #6895 |
What did I say Janine?
You wouldn't like it if I were angry... |
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06/22/2011 01:06:30 PM · #6896 |
| Oh, calm down or Joe might shoot you again, lol! |
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06/22/2011 01:10:00 PM · #6897 |
This place is now a gun free zone.
...or maybe a free gun zone.
...free gum zone?
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06/22/2011 01:38:46 PM · #6898 |
its my birthday today. For my birthday all I want is to be the last one to post in this thread. So by giving me nothing I will be very happy. Giving me an additional post after this one will make me unhappy.
That is all.
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06/22/2011 02:04:15 PM · #6899 |
Happy Birthday, Craig! Just sayin'.... No presents for YOU!
Actually I came because I heard there was free gum.... |
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06/22/2011 02:16:35 PM · #6900 |
| I heard there was gum shoe here??? |
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