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Math Help - graph theory help

  1. #1
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    graph theory help

    I have a couple of questions.

    1) I'm checking whether two graphs are isomorphic. They have the same number of vertices and edges, they have an equal number of vertices of a certain degree, and I can't construct an isomorphism. I'm lost.
    However, one of them has a 3-cyle, while the other one does not. Does this mean anything?

    2) Let G be a bipatite graph with 8 vertices and 13 edges. Prove that G is not planar.

    3) Let G be a simple graph with v>=2 vertices and e edges, If e<v-1, prove that G is not connected.
    Edit: I think I got this one.
    Assume that G is connected. Then it contains a spanning tree T. For every tree T: e(T)=v(T)-1, so we have e(G)>=e(T)=v(T)-1, which is a contradiction.

    Thank you for your help!
    Last edited by georgel; May 5th 2009 at 02:39 AM.
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  2. #2
    Junior Member
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    2) Let G be a bipatite graph with 8 vertices and 13 edges. Prove that G is not planar.

    I got this one as well.

    I still need help with the first one, though..
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