Question: 1. Prove that for a planar graph with k components, |V(G)|-|E(G)|+|F(G)| = 1+k.
2. Prove that the Petersen graph (shown in Figure) is not planar.
![532_26.jpg](https://secure.tutorsglobe.com/CMSImages/532_26.jpg)
3. Show that if every face of a planar graph has four edges, then |E(G)| = 2|V(G)| -4.
4. For which n is Kn planar and for which n is Kn non planar? Make and prove a conjecture.