For each of following degree sequences, price that the simple graph with 7 vertices exists or doesn't 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) 3, 3, 3, 3, 3, 3, 5
c) 2, 3, 4, 4, 4, 4, 5