COS 226 PROBLEM SET 9

1. [Exercise 26.4] Consider the graphs defined by the following sets of edges: 
  A.  0-1 0-2 0-3 1-3 1-4 2-5 2-9 3-6 4-7 4-8 5-8 5-9 6-7 6-9 7-8
  B.  0-1 0-2 0-3 0-3 1-4 2-5 2-9 3-6 4-7 4-8 5-8 5-9 6-7 6-9 7-8
  C.  0-1 1-2 1-3 0-3 0-4 2-5 2-9 3-6 4-7 4-8 5-8 5-9 6-7 6-9 7-8
  D.  4-1 7-9 6-2 7-3 5-0 0-2 0-8 1-6 3-9 6-3 2-8 1-5 9-8 4-5 4-7
Which of these graphs are isomorphic to one another?


2. Show, in the style of Figure 26.21, the DFS forest that results from a standard adjacency-matrix DFS
of the graph 0-1 1-2 1-7 2-0 2-4 3-2 3-4 4-5 4-6 4-7 5-3 5-6 7-8 8-6 8-7







3. Give the vertex connectivity and the edge connectivity of the graph in the previous question.


4. Show, in the style of Figure 27.9, the DFS forest that results from a standard adjacency-lists DFS
of the digraph 0-1 1-2 1-7 2-0 2-4 3-2 3-4 4-5 4-6 4-7 5-3 5-6 7-8 8-6 8-7







5. Give the transitive closure of the digraph in the previous question.






6. What is the result of using the source-queue topological sorting method on a DAG that is a directed tree, with all edges pointing away from the root?




Due: in precept on April 26 or 27.

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