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Math Help - Euler's formula + Handshake Theorem

  1. #1
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    Euler's formula + Handshake Theorem

    Using Euler's formula and the Handshake Theorem, how can I show that this graph is non-planar?
    Last edited by Natasha1; May 16th 2006 at 10:25 AM.
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  2. #2
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    The number of vertices is 8
    The number of edges is 14
    The number of faces is f
    Then, 8-14+f=2 if planar.
    Thus,
    f=8
    Which is not true.

    I did it this way because I was too lazy counting all the faces.
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  3. #3
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    I actually counted 21 edges, am I wrong?

    Euler's formula states that v+f = e+2

    Here

    v=8
    e=21
    f=?

    so 8+f=21+2
    f=15 which is not true as there are many more. Hence the graph is non-planar.

    Using the Handshake Theorem that states that 2e >= 3f
    we get ( 2(21) )/ 3 >= f which gives f <= 14 which again is not true, hence the graph is non-planar.

    Am I correct?
    Last edited by Natasha1; May 17th 2006 at 08:03 AM.
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