Practice Introduction To Graph Construction (4.2.1)

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9 questions

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6 sample questions

Question 1.
Define vertex connectivity in your own words.
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Think about what happens if you remove vertices.
Question 2.
What does edge connectivity represent?
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Consider the edges that connecting vertices.
3Question 3.
What is the minimum number of vertices that must be removed to disconnect a graph called?
- Vertex Connectivity
- Edge Connectivity
- Minimum Degree
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Focus on vertex removals.
4Question 4.
True or False: Edge connectivity is always greater than minimum degree.
- True
- False
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Think of a sparse versus a dense graph.
Question 5.
Design a graph with given parameters: vertex connectivity 4, edge connectivity 3, and minimum degree 5. Provide a detailed construction process.
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Identify the initial complete graphs and think about how many edges you need to add.
Question 6.
Prove that a graph with vertex connectivity k must have a minimum degree of at least k.
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Use examples with varying connections to illustrate.

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