Exercise 2.
For each degree sequence below, decide whether it must always, must never, or could possibly be a degree sequence for a tree. Remember, a degree sequence lists out the degrees (number of edges incident to the vertex) of all the vertices in a graph in non-increasing order.
\(\displaystyle (4,1,1,1,1)\)
\(\displaystyle (3,3,2,1,1)\)
\(\displaystyle (2,2,2,1,1)\)
\(\displaystyle (4, 4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1)\)