SECTION 4.2 Basics of Group Theory 209
(i) Give an automorphismσ which takes vertex 1 to vertex 2 by
completing the following:σ:
1 2 3 4 5 6
↓ ↓ ↓ ↓ ↓ ↓
2
Compute the inverse of this automorphism.(ii) Give an automorphismτ which maps vertex 1 to 3 and fixes
vertex 5 (that isτ(5) = 5).τ :
1 2 3 4 5 6
↓ ↓ ↓ ↓ ↓ ↓
3 5
Compute the inverse of this automorphism.- Consider the graph shown below.