Euler's formula + Handshake Theorem

[Natasha1]

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

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?

 

[shmoe]

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!

 

[rhj23]

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?