Bridges
Definition
A bridge in graph theory is an edge whose removal increases the number of connected components in the graph. It plays a critical role in determining the connectivity of a graph.
5 Must Know Facts For Your Next Test
- A bridge is also known as a cut-edge or an isthmus.
- Removing a bridge from a connected graph makes the graph disconnected.
- Bridges are crucial for understanding Euler Trails, as their presence affects the ability to form such trails.
- In any cycle, no edge is a bridge since removing it does not disconnect the cycle.
- Identifying bridges helps in analyzing network vulnerabilities and designing robust networks.
Review Questions
- What happens to a connected graph when you remove a bridge?
- Why are bridges important when studying Euler Trails?
- Can an edge in a cycle be considered a bridge? Why or why not?
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Related terms
Term: Euler Trail
Term: Connected Component
Term: Cut Vertex
