This question uses graph theory:

[10 pts] Let n E 2+ and let A, B , C be three pairwise disjoint sets, each of them having n elements. Construct a graph G 2 (V, E) as follows. The set of vertices is V = A U B U C and the set of edges E is dened by 0 There is an edge between every vertex in A and every vertex in B. I There is an edge between every vertex in B and every vertex in C. 0 There is an edge between every vertex in C and every vertex in A. c There are no other edges except those specied above. (a) [5 pts] Express the number of edges of G' in terms of n. Justify your answer . (b) [5 pts] Express the length of a longest cycle in G in terms of n. Justify your