Maximum and minimum number of articulation points in a graph with n nodes What's the maximum and minimum number of articulation points in a graph with n nodes? 
I think the maximum is n - 2 because the graph would be a straight line, and the nodes at the two ends can't be articulation points because they don't have children. 
I think the minimum is 0 because you can have a complete graph and if you remove any of the nodes the rest of the nodes are still connected. 
However I can't prove that my answer is correct. 
What's the correct answer and how do you prove it? 
 A: You are almost done, your results are fine
(except that you need to make a trivial exception for $n=1$).
You have already shown that the maximum is at least $n-2$.
To prove that the maximum is at most $n-2$, we show that every graph has at least two vertices that are NOT articulation points.
This follows from three observations:
1) An isolated vertex is never an articulation point.
2) A connected graph with at least two vertices has at least 2 vertices that are not articulation points
3) The number of non-articulation points in a disconnected graph equals the sum of the number of non-articulation points in its components.
Only the second item requires some justification, the others are obvious.
For the second item we recall the facts that every connected graph has a spanning tree, that a leaf in a tree is never an articulation point (for the tree),
and that a tree with at least two vertices has at least two leaves.
So a spanning tree has at least two vertices that are not articulation points(for the tree, so certainly not for the entire graph).
