Use the graphs on the following page to answer these questions. 1. (7 points) For graph 1, list the vertices of a depth-first search starting at vertex A. Choose the alphabetically lower vertex when you have a choice. 2. (7 points) For graph 1, list the vertices of a breadth-first search starting at vertex A. Choose the alphabetically lower vertex when you have a choice. 3. (4 points) Determine the chromatic number for graph 2. Provide a coloring for the graph. For each color, provide a list of vertices that have been assigned that color. 4. (7 points) Using graph 3, list the shortest path from vertex A to each of the other vertices in the graph. 5. (7 points) Find a minimum spanning tree in graph 3. B H . ( E Graph 1 B H Graph 2 6 A 4 E 2 3 2 B 8 6 G F 5 1 4 7 7 H 1 Graph 3