Let T be the tree with Prüfer code 3, 2, 1, 3, 2, 1. (a) Give the number of vertices of T, and the number of vertices that are leaves. Justify your answers. (b) Does T contain a 3-4-walk of length 2? Justify your answer. (c) What is the number of distinct trees with vertex set V(T)? Justify your answer. (d) What is the number of distinct graphs that have T as a spanning tree? Justify your answer. (e) Give an efficient algorithm that, for any sequence d1, d2, ..., dn that is the degree sequence of a tree, constructs a particular tree with that degree sequence. Explain briefly why the algorithm is correct and efficient.