Question about the conditions to find articulation points in a graph
Here is the proof:
Given we have A -&gt; B as an edge where A is not the root, let's assume A is an articulation point thats not the root. Removing it results in 2 subsets - the first containing the root and the second containing B.
For the subset containing B to be disjoint from the root if A is removed, B should not have a link to any node from root ... A that is it should not be able to reach a vertex higher than itself. This is possible only if:

A -&gt; B is a bridge meaning the highest node reachable from B is itself
A is the only node B is connected to that is above it. This way if we remove A the highest node reachable from B is itself.