1. How many edges does the complete graph with 11 vertices have? 2. A certain graph is bipartite, with vertices colored blue and red. Each blue vertex has degree 15; each red vertex has degree 10. The graph has 75 vertices altogether. How many red vertices are there? 3. True or False? No graph with exactly four vertices has both an Eulerian circuit and a Hamiltonian cycle. 4. How many graphs having the vertex set {1,2,3,4,5} are there? (Hint: Some such graphs may be isomorphic, without being the same graph; if they are not the same graph, they get counted separately. It is more difcult to nd the maximum possible number of nonisomorphic graphs having that vertex set, but that is not the problem here.) 5. How many graphs having the vertex set {1, 2, 3, 4, 5} have exactly 5 edges? 6. True or False? No graph having exactly 8 vertices has both a vertex of degree 0 and a vertex of degree 7. 7. True or False? There is a graph that has the degree sequence 7, 6, 5, 4, 3, 2, 1,0