2. Degree Sequences (30 points). You are given two sequences of non-negative integers below. Decide which sequences below represent the degree sequence of some simple graph. To receive credit for this problem you must show all of your work, write complete sentences, be precise and clear, and include ALL details. Not following instructions will lead to massive point deductions. (a) Is s = 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 the degree sequence of some simple graph G? YES or NO (circle one) If your answer is YES then draw G. If your answer is NO then prove that s cannot be the degree se- quence of any graph. (b) Is s = 5, 4, 3, 2, 1 the degree sequence of some simple graph G? YES or NO (circle one) If your answer is YES then draw G. If your answer is NO then prove that s cannot be the degree se- quence of any graph