List of top Algorithms Questions on Graph traversals asked in GATE CS

Consider the following pseudocode for depth-first search (DFS) algorithm which takes a directed graph \(G(V,E)\) as input, where \(d[v]\) and \(f[v]\) are the discovery time and finishing time, respectively, of the vertex \(v \in V\).
DFS(G):
  unmark all v in V
  t <- 0
  for each v in V
    if v is unmarked
      t <- Explore(G, v, t)
    end if
  end for

Explore(G, v, t):
  mark v
  t <- t + 1
  d[v] <- t
  for each (v, w) in E
    if w is unmarked
      t <- Explore(G, w, t)
    end if
  end for
  t <- t + 1
  f[v] <- t
  return t
Suppose that the input directed graph \(G(V,E)\) is a directed acyclic graph (DAG).
For an edge \((u,v) \in E\), which of the following options will NEVER be correct?
Consider a complete binary tree with 7 nodes. Let \( A \) denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let \( B \) denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root. The value of \( |A - B| \) is \(\underline{\hspace{2cm}}\).

Consider the following directed graph: 
Which of the following is/are correct about the graph? 

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?