(Solved): Problem 2. \( (12 \mathrm{pts}=2 \times 6) \) The degree sequence of a graph is the sequence of th ...

Problem 2. \( (12 \mathrm{pts}=2 \times 6) \) The degree sequence of a graph is the sequence of the degrees of the vertices of the graph in nonincreasing order. For example, the degree sequence of the graph \( \mathrm{G}_{1} \) in problem 1 is \( 3,3,2 \), \( 2,1,1,1,1 \). A sequence \( d_{1}, d_{2}, \ldots, d_{n} \) is called graphic if it is the degree sequence of a simple graph. Determine whether each of the following sequences is graphic. For those that are, draw a graph having the given degree sequence. If not graphic, explain why not. a) \( 3,3,3,3,2 \) b) \( 5,4,3,2,1 \) c) \( 4,4,3,2,1 \) d) \( 4,4,3,3,3 \) e) \( 3,2,2,1,0 \) f) \( 1,1,1,1,1 \)