28.1.1 - Vertex and Edge Connectivity
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Practice Questions
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Define vertex connectivity.
💡 Hint: What does κ(G) represent?
What is a vertex cut?
💡 Hint: Think about how many vertices you need to remove.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a vertex cut?
💡 Hint: Think about what needs to be removed to disconnect.
True or False: The edge connectivity of a disconnected graph is 1.
💡 Hint: Consider what happens in a graph that is already disconnected.
1 more question available
Challenge Problems
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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.
💡 Hint: Analyze how the removal affects the connectivity of other vertices.
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.
💡 Hint: Consider the structure and degree of vertices.
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