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Euler's formula + Handshake Theorem

  1. May 17, 2006 #1
    Using Euler's formula and the Handshake Theorem, how can I show that this graph is non-planar? (see graph attached)

    My answer:

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



    so 8+f=21+2
    hence 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?

    Attached Files:

    Last edited: May 17, 2006
  2. jcsd
  3. May 17, 2006 #2


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    Attatchment is still pending approval, but this is just a matter of counting right? I mean you know if it's planar e, v, and f satisfy some simple relations, therefore if they don't satisfy them it's not planar. Have some confidence!
  4. May 18, 2006 #3
    rather than using the two theorems to get results, then say that they are not true, would it not be better to use the fact that they are contradictory?
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