Using Euler's formula and the Handshake Theorem, how can I show that this graph is non-planar? (see graph attached)(adsbygoogle = window.adsbygoogle || []).push({});

My answer:

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

Here

v=8

e=21

f=?

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?

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# Euler's formula + Handshake Theorem

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