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Math Help - One More Trees Problem

  1. #1
    Senior Member
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    One More Trees Problem

    A certain tree T of order n has only vertices of degree 1 and 3. Show that T contains (n-2)/2 vertices of degree 3.

    Well I know it will have n-1 edges.

    I also know by the first theorem of graph theory
    that

    sum (deg vertices)=2(size)=2(n-1)

    I can let x=number of vertices of degree 1 and n-x=number of degree 3.

    So

    x+(n-x)=2(n-1), but then I get confused because the x's cancel and I have

    n=2n-2

    Or

    n-2=0
    n=2...That doesn't make sense though...what is wrong?

    Nevermind, I got it...I forgot it was 3x
    Last edited by zhupolongjoe; October 4th 2009 at 07:58 AM. Reason: Solved
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