## Description

1. Find a topological sort for the graph in file hw9_top_sort.jpg.

10 points

2. For the graph in the file hw9_graph_letters.jpg, give a path of a breadth-first search,

starting from vertex I.

20 points

3. Find the single-source shortest path from Home to all of the other locations in the graph in

file hw9_points_of_interest.jpg. Show each step as in slides 57 to 64.

20 points

4. Find the maximum flow for from JCT A to JCT G for the graph in file hw9_dag_junctions.jpg.

Show each step as in slides 84 to 85.

10 points

5. Find the minimum spanning tree using Prim’s algorithm for the graph in file hw9_points_of_interest.jpg. Show each step as in slide 89.

10 points

6. Repeat #5 using Kruskal’s algorithm. Show each step as in slide 100.

10 points

7. Produce a depth-first spanning tree for the graph in file hw9_graph_dfs.jpg.

Show as in slide 124, labeling Num(v) and Low(v) for each vertex and identifying

all articulation points.

10 points

8. For the graph in the file hw9_graph_letters.jpg, does it have an Euler Path or Euler Circuit?

If it does, give the sequence of letters for it.

#### Submit to eLearning:

hw9.doc (.doc can be .txt, .jpg, etc.)