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?