DFS Tree Example

Graph: $1-2$, $2-3$, $3-1$, $2-4$. Start DFS at $1$. Tree edges: $1-2$, $2-3$, $2-4$. Back edge: $3-1$ (connects $3$ back to ancestor $1$). Edge $2-4$ is a bridge because there is no back edge providing an alternate path to $4$.

Vertex $4$ is a dead end. Edges $1-2$ and $2-3$ are not bridges because back edge $3-1$ creates a cycle, providing an alternate path between any two vertices in the triangle.