Euler's formula + Handshake Theorem

  • Thread starter Natasha1
  • Start date
  • #1
467
7
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?
 

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Answers and Replies

  • #2
shmoe
Science Advisor
Homework Helper
1,992
1
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!
 
  • #3
20
0
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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