A sequence of natural numbers (a1, a2, ..., an) is said to be a degree sequence if there exists an undirected graph on n vertices {v1, v2, ..., vn} such that the degree of vi is ai for each i = 1, 2, ..., n.
(a) is (0, 1, 1, 1, 2, 2, 3, 4) a degree sequence? Justify your answer.
(b) is (0, 1, 1, 1, 2, 3, 3, 4) a degree sequence? Justify your answer.