Practice Vertex And Edge Connectivity (28.1.1) - Vertex and Edge Connectivity

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9 questions

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6 sample questions

Question 1.
Define vertex connectivity.
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What does κ(G) represent?
Question 2.
What is a vertex cut?
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Think about how many vertices you need to remove.
3Question 3.
What is a vertex cut?
- A single vertex
- A group of edges
- A subset of vertices
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Think about what needs to be removed to disconnect.
4Question 4.
True or False: The edge connectivity of a disconnected graph is 1.
- True
- False
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Consider what happens in a graph that is already disconnected.
Question 5.
Consider a graph with vertices {A, B, C, D, E} and edges {AB, AC, AD, BE, CE}. Determine whether the following sets are vertex cuts: {B}, {A, C}. Explain your reasoning.
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Analyze how the removal affects the connectivity of other vertices.
Question 6.
In a connected, non-complete graph with 5 vertices, prove that if the minimum degree is 2, then κ(G) ≤ 2. Provide an example graph to illustrate your answer.
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Consider the structure and degree of vertices.

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