Wikipedia:Reference desk/Archives/Mathematics/2009 March 11

= March 11 =

number of spanning trees of K_n-e
Hello. I want to use Cayley's formula to show that the number of spanning trees in the labeled graph Kn-e is (n-2)nn-3. Here e is any edge in Kn. Can someone point me in the right direction please. Equivalently I want to figure out the number of spanning trees involving the edge e.--Shahab (talk) 06:23, 11 March 2009 (UTC)


 * You know there are $$n^{n-2}$$ spanning trees altogether. Choose one at random.  What is the probability that it includes e? McKay (talk) 07:37, 11 March 2009 (UTC)
 * $$\frac{n-1}{\frac{n(n-1)}{2}}$$. Now what?--Shahab (talk) 07:56, 11 March 2009 (UTC) OK I got it. Thanks for the tip. Cheers--Shahab (talk) 08:03, 11 March 2009 (UTC)