Question

identify all edges on the graph that are bridges.

the edges □ are bridges.
(use a comma to separate answers as needed )

Explanation:

Step1: Recall the definition of a bridge

A bridge in a graph is an edge whose removal increases the number of connected components.

Step2: Analyze each edge

• Edge \(AB\): Removing \(AB\) would separate the cycle - like part (with \(C\)) from the rest of the graph.
• Edge \(BD\): Removing \(BD\) would separate the left - hand sub - graph (with \(A\) and \(C\)) from the right - hand sub - graph (with \(E\) and \(F\)).
• Edge \(DE\): Removing \(DE\) would not increase the number of connected components since \(D\) and \(E\) are still connected through other paths (if there were any, but in this case, removing \(DE\) does increase the components as there is no alternative path).
• Edge \(DF\): Removing \(DF\) does not increase the number of connected components as \(D\) and \(F\) are part of a triangle - like sub - structure (\(D - E - F\)).
• Edge \(AC\): Removing \(AC\) does not increase the number of connected components as \(A\) and \(C\) are still connected through \(AB\).
• Edge \(BE\): There is no edge \(BE\) in the given graph.

Answer:

\(AB\), \(BD\)