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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define vertex connectivity.
💡 Hint: What does κ(G) represent?
Question 2
Easy
What is a vertex cut?
💡 Hint: Think about how many vertices you need to remove.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a vertex cut?
- A single vertex
- A group of edges
- A subset of vertices
💡 Hint: Think about what needs to be removed to disconnect.
Question 2
True or False: The edge connectivity of a disconnected graph is 1.
- True
- False
💡 Hint: Consider what happens in a graph that is already disconnected.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation