Questions: Identify all edges on the graph that are bridges. The edges are bridges. (Use a comma to separate answers as needed.)

Identify all edges on the graph that are bridges. The edges are bridges. (Use a comma to separate answers as needed.)
Transcript text: Identify all edges on the graph that are bridges. The edges $\square$ are bridges. (Use a comma to separate answers as needed.)
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Solution

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Solution Steps

Step 1: Definition of a bridge

A bridge is an edge that, if removed, increases the number of connected components in the graph.

Step 2: Analyzing the edges

  • Removing AB: The graph becomes disconnected, with A in one component and the rest of the vertices in another component. Thus, AB is a bridge.

  • Removing BC: The graph becomes disconnected, with A and B in one component and C, D, E, and F in another component. Thus, BC is a bridge.

  • Removing CD: The graph remains connected. Thus, CD is not a bridge.

  • Removing DE: The graph remains connected. Thus, DE is not a bridge.

  • Removing DF: The graph remains connected. Thus, DF is not a bridge.

  • Removing EF: The graph remains connected. Thus, EF is not a bridge.

Final Answer

The edges AB, BC are bridges. \\( \boxed{\text{AB, BC}} \\)

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