Q41

MCQ2 marks, −0.67

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 $\text{DFS}$ tree obtained by doing $\text{DFS}$ 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 $u$ .

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