1) Give the degree sequence for P4 2

1) Give the degree sequence for P4 2. Is the following sequence graphic? If yes, give a graph. If not, explain why. {1,2,2,3,4} 3. What restrictions are required for a degree sequence to be valid (also called graphic)? 4. Is it possible for a graph to have both a vertex of degree 0 and a vertex of degree n-1? Explain why or why not in your own words (no proof required) 5. In any graph, how many allowable degrees are there? That is, how long is the list of all possible degrees? 6. Prove the following: If G is a connected simple graph, then there must be two vertices of the same degree.