For each of the following degree sequences, prove that a simple graph with 7 vertices exists or does not exist by either drawing such a graph or showing mathematically that such a

graph is impossible.

(a) 1,1,2,3,4,5,6.

(b) 0,0,2,3,4,5,6.

(c) 1,1,3,3,3,5,5.

(d) 3,3,3,3,3,3,6.

(e) 3,3,3,3,4,4,6.

(f) 2,3,4,4,4,4,5.