Find and draw two graphs on 6 vertices that have the same degree sequence but are not isomorphic.
6. The Degree Theorem says that in any graph, the sum of all the degrees is equal to twice the number of edges. How would you state this theorem in terms of the adjacency matrix of a graph?
7. The distance between two vertices in the same component of a graph is the length of the shortest path joining these vertices. If G is a connected graph, the diameter of G is the maximum of all of the distances between vertices of G. Suppose that the graph G2 is the complement of the graph G1. Show that one of G1 or G2 must be a connected graph, by showing that if G1 is disconnected, then the diameter of G2 is at most 2.