A graph is a set of points called vertices connected by lines called edges. Here is a graph called the Petersen graph.

0
/|\
/ | \
/ | \
/ | \
/ | \
/ 5 \
/ / \ \
/ / \ \
1---6-+-----+-9---4
| \| |/ |
| X X |
| |\ /| |
| | \ / | |
| | X | |
| | / \ | |
| |/ \| |
| 7 8 |
| / \ |
| / \ |
| / \ |
| / \ |
|/ \|
2-----------------3

An automorphism of a graph G is a function f:G→G such that f(xy)=f(x)f(y) for all x, y∈G. A vertex-transitive graph is a graph G such that there is an automorphism between any two vertices of G. An edge-transitive graph is a graph G such that there is an automorphism between any two edges of G.

1. Prove that the Petersen graph is vertex-transitive.

2. Prove that the Petersen graph is edge-transitive.