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12.5. Independent Set Problem

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  1. 1.

    Define what an independent set is.

    Hint

    Think about the connections between vertices.

  2. 2.

    Can a single vertex form an independent set?

    Hint

    Consider whether it has edges connecting to anything else.

  3. 3.

    What defines an independent set?

    • Connected vertices
    • Unconnected vertices
    • Vertices with edges
    Hint

    Think about how edges relate to vertices.

  4. 4.

    True or False: An independent set can contain two directly connected vertices.

    • True
    • False
    Hint

    Recall what makes a set independent.

  5. 5.

    Given a complex graph with vertices numbered from 1 to 10 and edges connecting every vertex to two others, determine the largest possible independent set and justify your reasoning.

    Hint

    Consider connections carefully before making selections.

  6. 6.

    Construct a graph and demonstrate two different independent sets within it. Highlight the differences in edge connections.

    Hint

    Map edges clearly to visualize independence.

Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

4 more questions available

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Quiz

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

1 more question available

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Challenge Problems

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting