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Question Description

  1. Consider the following directed graph, which is given in adjacency list form and where vertexes have numerical labels:

    1: 2, 4, 6
    2: 4, 5
    3: 1, 2, 6, 9
    4: 5
    5: 4, 7
    6: 1, 5, 7
    7: 3, 5
    8: 2, 6, 7
    9: 1, 7
    

    The first line indicates that the graph contains a directed edge from vertex 1 to vertex 2, from 1 to vertex 4, and 1 to 6, and likewise for subsequent lines.

    Part A: What is the degree of node 3?

    Part B: List the nodes in the order they’re visited by depth-first search starting at vertex 4. When choosing successors, use the 367 convention of increasing numerical order.

    Part C: Show the corresponding breadth-first search spanning tree for the graph above starting at vertex 3. When choosing successors, use the 367 convention of increasing numerical order. Draw your tree either graphically or in the same manner using characters as done in prior assignments. Verify that your trees in the pdf file looks okay before submitting.

  2. Consider the following directed graph, which is given in adjacency list form as described above and where vertexes have numerical labels:

    1: 3, 5
    2: 6
    3: 6
    4: 6, 7
    5: 7, 8
    6: 
    7: 8 
    8: 9
    9:
    

    Show the topological ordering for the graph above when using the 367 convention of choosing vertexes in increasing numerical order.

  3. Consider the following undirected graph, which is given in adjacency matrix form and where vertexes have character labels and edges have non-negative integer weights (no value indicates no edge exists):

        A B C D E F G
      +--------------
    A |   2 8 4
    B | 2     1 7
    C | 8         3 5
    D | 4 1     3
    E |   7   3   1
    F |     3   1   8
    G |     5     8
    

    Part A: What is the degree of node F?

    Part B: Trace Dijkstra’s algorithm starting at node C by completing the table started below where each row represents one iteration of the algorithm.

    Iteration List of Visited Vertexes and their
    shortest distances from start
    Priority Queue’s items
    (listed in increasing order)
    0 0 C
    1 C 0 3 F, 5 G, 8 A
    2 C 0, F 3  
  4. Part C: What is the shortest path from C to A? Give a list of vertexes starting at C and ending at A.

    Part D: What is the shortest path from C to D? Give a list of vertexes starting at C and ending at D.

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