Question

identify all edges on the graph that are bridges.

the edges \square are bridges
(use a comma to separate answers as needed )

Explanation:

Step1: Recall the definition of a bridge

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

Step2: Analyze each edge

• Edge \(AB\): Removing \(AB\) would separate the part of the graph with \(A\) (since \(A\) has a loop, but the loop doesn't affect connectivity in the sense of bridge - the key is the connection to the rest of the non - loop part). The rest of the graph (\(B,C,D,E,F\)) is still connected without \(AB\).
• Edge \(BC\): Removing \(BC\) leaves the graph still connected. For example, we can go from \(B\) to \(D\) to \(E\) etc.
• Edge \(BD\): Removing \(BD\) leaves two sub - graphs: one with \(B,C\) and one with \(D,E,F\).
• Edge \(DE\): Removing \(DE\) still leaves the graph connected (e.g., \(D - F - E\) path if \(DE\) is removed).
• Edge \(DF\): Removing \(DF\) still leaves the graph connected (e.g., \(D - E - F\) path if \(DF\) is removed).
• Edge \(EF\): Removing \(EF\) still leaves the graph connected (e.g., \(E - D - F\) path if \(EF\) is removed).

Answer:

\(BD\)