Hello. I recently had an Algebra exam that had a few questions about graph automorphisms. I'm not too familiar with graphs (a little bit familiar with permutations, groups, and morphisms though) so I was hoping someone could help me out with these questions and/or maybe lead me to any online resources about the subject since my textbook doesn't say much about it.

1) Let

be the graph on 4 vertices with edges {1,2} and {3,4} (union of two disjoint edges). Make a list of all elements in the automorphism group of

This one seems easiest, so if someone could explain how to go about this maybe I would understand the concept a bit better and try figuring out the other two.

2) Let

be the union of

*n* disjoint edges (on 2n vertices) and

. Determine the order

I think the answer to this one was

but I'm not sure how to get at that.

3) (Follow up to 2) Let

in the preceding problem. Describe all the elements of order 3 in

. How many are there?

Again on this one I know the answer is 8 elements of order 3, but have no idea how to find that. The elements are listed as permutations and I know the elements of order three are products of disjoint 3 cycles, but I don't know how to find them.

I'd greatly appreciate any help, since I'm not really familiar with graphs at all.