[10 pts] This problem will use the concept of a graph's degree sequence. This is a list of the

degrees of all the vertices in the graph, in descending order of degree. For example, the

graph

a

C

(†)

has degree sequence (4,3,3,2,2,0) because there is one node with degree 4 (c), two nodes with

degree 3 (b and d), two nodes with degree 2 (a and e), and one node with degree 0 (f).

For each of the following, either list the set of edges of a tree with vertex set {a, b, c, d, e, f}

that has the stated degree sequence, or show that no such tree exists. There's no need to draw

out the tree here, but it may help you to do so on paper.

(a) [4 pts] (3,3,3,1, 1, 1)

(b) [4 pts] (3,3,1, 1, 1, 1)

(c) [4 pts] (4,3, 1, 1, 1, 1)