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3 cards from this section. Quick, good the night before a test.
What is vertex connectivity?
Think about removing points to create isolation.
Define edge connectivity.
Consider how many connections you need to sever.
What must be true about vertex connectivity compared to edge connectivity?
Review the properties discussed about connectivity.
True or False: The minimum degree of a graph is always less than or equal to its vertex connectivity.
Consider the definitions of degree and connectivity.
Prove that for a simple graph with vertex connectivity l and edge connectivity m, if l > m, the graph must contain at least one cut vertex.
Use contradiction by assuming a scenario where no cut vertices exist.
Construct a non-complete graph that meets the criteria: vertex connectivity = edge connectivity = 3, and state why it is not complete.
Consider structures like cycles or trees that meet the conditions.
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