GATE | GATE CS 2021 | Set 1 | Question 51

An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following options is/are correct?

(A)

Root of T can never be an articulation point in G.

(B)

Root of T is an articulation point in G if and only if it has 2 or more children.

(C)

A leaf of T can be an articulation point in G.

(D)

If u is an articulation point in G such that x is an ancestor of u in T and y is a descendent of u in T, then all paths from x to y in G must pass through u.

Answer

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