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December 9th, 2009, 06:37 AM   #1
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Spanning and Induced Subgraphs

Let G be a complete graph on n vertices.
a. How many spanning subgraphs does G have?
b. How many induced subgraphs does G have?
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December 9th, 2009, 06:54 AM   #2
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Re: Spanning and Induced Subgraphs

Do the spanning graphs need to be connected? Are the vertices labeled? (i.e. are two isomorphic graphs with different vertices considered the same?)

An induced subgraph will be complete. How many complete graphs with at most n vertices are there?

In any case, for the first question, you are just removing edges and for the second, just vertices. Count the ways to this.
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