Recently I came across this problem from IARCS Problem Archive , and after some research , the answer seems to be tarjan's algorithm to find the points which when deleted , breaks the graph in two or more smaller graphs .

Here is this article "Articulation Points (or Cut Vertices) in a Graph " on that algorithm from geeks for geeks , but what is the use of that time variable and the arrays disc and low , why do we need to maintain them?