Practice Conclusion (28.1.8) - Vertex and Edge Connectivity - Discrete Mathematics

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6 sample questions

Question 1.
Define vertex cut in your own words.
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Think about what happens when you take away certain vertices.
Question 2.
What does edge connectivity refer to?
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Consider why you might want to remove edges.
3Question 3.
What is a vertex cut?
- A collection of edges
- A collection of vertices
- A subgraph
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Think about what parts of a graph can be removed to cause disconnectivity.
4Question 4.
Edge connectivity is represented by which symbol?
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Consider symbols commonly used in mathematics.
Question 5.
Given a connected graph with 7 vertices, where vertex A is connected to B, C, D, and E, while B connects back to A, C, and F, and C further connects to G. Find and justify the vertex cut(s).
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Check how connections work before and after removal.
Question 6.
For any arbitrary connected graph, prove or disprove that at least one vertex cut exists. Provide reasoning.
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Think about the structure of the graph.

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