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The graph theory HELP

  1. Apr 8, 2009 #1
    The graph theory HELP!!!

    How many distinct graphs can be found by the set V={1,2,....,n} with k edges?

    For this question i conclude that totao.l number of distinct graphs comes with 2^(choose two in n)

    but i cannot find the solution which gives the relation with k edges can you help me?
     
  2. jcsd
  3. Apr 8, 2009 #2
    Re: The graph theory HELP!!!

    There are a total of (n^2 - n)/2 = 1/2 n(n-1) pairs of vertices. You pick k out of these, so you have Comb(1/2 n(n-1), k) possibilities.

    If you're talking about directed graphs, multiply this by 2. If you allow for loops, take 1/2 n^2 instead of 1/2 n(n-1).
     
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