Question 9 from GGT: This problem gives you practice with orbits and stabilizers and thinking about graphs. Let I be the Petersen graph, and assume that Sym(r) = Symg. Prove that if v is a vertex of I', then IStab(v)| = 12. Can you determine which group of order 12 this is? Question 12 from GGT: This problem gives you practice with multiplying cycles and thinking about the symmetric group. The group A, is the subgroup of the group Sym, that consists of even permutations (even numbers of transpositions.) We consider the identity an even permutation, so it is in A. The first published Cayley graph, appearing in Cayley's paper form 1878, was the Cayley graph for A, with respect to the generating set ((123), (234)). Draw this Cayley graph.

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