A sequence of natural numbers a1 a2 an is said to be a

Question

A sequence of natural numbers (a₁, a₂, ..., a_n) is said to be a degree sequence if there exists an undirected graph on n vertices {v₁, v₂, ..., v_n} such that the degree of v_i is a_i 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.