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