 #1
 467
 7
Using Euler's formula and the Handshake Theorem, how can I show that this graph is nonplanar? (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 nonplanar.
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 nonplanar.
Am I correct?
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 nonplanar.
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 nonplanar.
Am I correct?
Attachments

16.2 KB Views: 319
Last edited: