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

1. A bridge is also known as a cut-edge or an isthmus.
2. Removing a bridge from a connected graph makes the graph disconnected.
3. Bridges are crucial for understanding Euler Trails, as their presence affects the ability to form such trails.
4. In any cycle, no edge is a bridge since removing it does not disconnect the cycle.
5. 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?

Related terms

Euler Trail: A trail in a graph that visits every edge exactly once

Connected Component: A maximal subgraph where there is a path between any two vertices

Cut Vertex: A vertex whose removal increases the number of connected components