Determine the number of distinct labelling

Question

1. Determine the number of distinct labelling of k_n,n. Do the same for K_m,m and k_m,n,l

2. Give an example of a graph G with the following characteristics:

(a) Aut(G) = {id}
(b) G is vertex-transitive, but not edge-transitive.
(c) G is edge-transitive, but not vertex-transitive.
(d) G is vertex-transitive and edge-transitive.
(e) G is neither edge-transitive nor vertex-transitive.