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Math Help - Connected components.

  1. #1
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    Question Connected components.

    G = (V,E) has v vertices, e edges and p connected components.
    Prove that e = (v - p)(v - p + 1)/2.
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  2. #2
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    There is something wrong with the formula you posted.
    Look at the attached graph. It has 2 components, 7 vertices, and 7 edges.
    Even if it were about maximal components there will be only two more edges in this graph. The formula still does not work.
    Attached Thumbnails Attached Thumbnails Connected components.-comp.gif  
    Last edited by Plato; October 18th 2007 at 11:44 AM.
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  3. #3
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    Quote Originally Posted by Plato View Post
    There is something wrong with the formula you posted.
    Look at the attached graph. It has 2 components, 7 vertices, and 7 edges.
    Even if it were about maximal components there will be only two more edges in this graph. The formula still does not work.
    Oh, I'm sorry!
    The true fromula is e <= (v - p)(v - p + 1)/2
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