Let X = (V, E) be a graph and let G

6. Let X 2 (ME) be a graph and let G g Aut(X). A map E : V ) {1,...,k} is called a k-labeling of X. A pair of labelings i, Z' are said to be equal (under G) if there exist some 9 E G such that NU) = [(9 ' v) for all 1) E V. (a) Let X be the 5-cycle and let G = Z5. Find the number of different (under G) 3-labelings of X. (b) Let X be the graph of Exercise 5(6) and let G = Q8. Find the number of different (under G) 2-1abelings of X