A bridge, ut-edge, or cut arc is an edge of a graph whose deletion increases its number of connected components.
Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
A graph is said to be bridgeless or isthmus-free if it contains no bridges.
If we remove {d,e} edge then there is no way to reach e and the graph is disconnected.
The removal of edges {c,d} and {c,f} makes graph disconnect but this forms a cycle.