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Has anyone found a method for counting the number of subgraphs of W3 without actually drawing out every graph and counting them?<br> --[[User:Aoser|Aoser]] 16:51, 3 November 2008 (UTC) | Has anyone found a method for counting the number of subgraphs of W3 without actually drawing out every graph and counting them?<br> --[[User:Aoser|Aoser]] 16:51, 3 November 2008 (UTC) | ||
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| + | Yep, I found. Build the adjacency matrix for W3.<br> 1) Consider (# ways to choose i vertices), where i=1,2,3,4.<br> 2) Also consider # places for edges in each configuration (with 1, 2, 3, 4 vertices) - build the edge or not (2 choices).<br> Combine these using product & sum rules.<br> Hope it helps<br>--[[User:Asuleime|Asuleime]] 22:45, 5 November 2008 (UTC) | ||
Revision as of 17:45, 5 November 2008
Has anyone found a method for counting the number of subgraphs of W3 without actually drawing out every graph and counting them?
--Aoser 16:51, 3 November 2008 (UTC)
--
Yep, I found. Build the adjacency matrix for W3.
1) Consider (# ways to choose i vertices), where i=1,2,3,4.
2) Also consider # places for edges in each configuration (with 1, 2, 3, 4 vertices) - build the edge or not (2 choices).
Combine these using product & sum rules.
Hope it helps
--Asuleime 22:45, 5 November 2008 (UTC)
