Edge versus vertex connectivity

Show that each vertex 2-connected graph is edge 2-connected.

(An edge 2-connected graph is such that after removing any edge remains connected.)

Solution
If the graph has a bridge and it is not \( K_2 \), then at least one of the ends of this bridge is adjacent to some other vertex and forms the articulation itself.
Variant
Find the smallest graph that is edge 2-connected but not vertex 2-connected.
Answer
The graph on five vertices obtained by merging two triangles in a vertex.
Variant
For any pair of integers \( k \geq l \geq 2 \) construct a graph of edge connectivity \(k\) and vertex connectivity \(l\).
Solution
Take two complete graphs \(K_{k+1}\) and merge them over \(l\) common vertices.

The smallest vertex cut are the \(l\) common vertices.

The smallest edge cut are the edges incident with any vertex of degree \(k\).