(Solved): The degree sequence of an undirected graph is the list of degrees of all vertices in decreasing or ...

The degree sequence of an undirected graph is the list of degrees of all vertices in decreasing order. (for example, the degree sequence of the graph G in question 5 is 3,3,3,3,2. There are five numbers there, because there are five vertices in the graph). Draw the only simple graph with the degree sequence 5, 3, 3, 3, 3, 3. Clearly label its vertices. (there is a unique graph with this degree sequence, others will be isomorphic copies. You DO NOT need to prove this) Now find a vertex to delete, so that the remaining graph has an Eulerian circuit. Draw the graph after removal of the designated vertex.