please answer 1,2,3,6,7

1. What are the possible values for m and n in a complete bipartite graph Km,n, if the number of edges is 20 ? Explain your answer. 2. Give an example or prove there are none: a. a simple undirected graph with 6 vertices and 16 edges. b. a simple undirected graph with 7 vertices that has an Euler circuit, but no Hamilton circuit. 3. How can an algorithm compute the number of edges in a pseudograph (where multiple edges and loops are allowed) from its adjacency matrix representation? 4. If the degree sequence of simple undirected graph G is 4,3,3,2, 2, what is the degree sequence of G ? 5. Exercises 44 and 70 on pages 712713 in the textbook. 6. Exercise 14 (point b and c only) on page 725 in the textbook. 7. In many cases, the vertex connectivity k(G) equals the smallest vertex degree in the graph (the graph can be disconnected by removing all neighbors of the vertex with the smallest degree). Show that this is not always true, by finding a graph G in which k(G) is different from the smallest vertex degree in G