Question 1 |

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?

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G.

Which of the following options is/are correct?

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

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

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

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. |

Question 1 Explanation:

Question 2 |

G is an undirected graph with vertex set {v1, v2, v3, v4, v5, v6, v7} and edge set {v1v2, v1v3, v1v4 ,v2v4, v2v5, v3v4, v4v5, v4v6, v5v6, v6v7 }. A breadth first search of the graph is performed with v1 as the root node. Which of the following is a tree edge?

v2v4 | |

v1v4 | |

v4v5 | |

v3v4 |

Question 2 Explanation:

Question 3 |

Which of the following is application of Breath First Search on the graph?

Finding diameter of the graph | |

Finding bipartite graph | |

Both (A) and (B) | |

None of the above |

Question 3 Explanation:

Question 4 |

Let G be a simple undirected graph. Let TD be a depth first search tree of G. Let TB be a breadth first search tree of G. Consider the following statements.

(I) No edge of G is a cross edge with respect to TD. (A cross edge in G is between two nodes neither of which is an ancestor of the other in TD.)

(II) For every edge (u,v) of G, if u is at depth i and v is at depth j in TB, then |i-j|=1.

Which of the statements above must necessarily be true?

(I) No edge of G is a cross edge with respect to TD. (A cross edge in G is between two nodes neither of which is an ancestor of the other in TD.)

(II) For every edge (u,v) of G, if u is at depth i and v is at depth j in TB, then |i-j|=1.

Which of the statements above must necessarily be true?

I only | |

II only | |

Both I and II | |

Neither I nor II |

Question 4 Explanation:

Question 5 |

The Breadth First Search (BFS) algorithm has been implemented using the queue data
structure. Which one of the following is a possible order of visiting the nodes in the graph
below?

MNOPQR | |

NQMPOR | |

QMNROP | |

POQNMR |

Question 5 Explanation:

Question 6 |

Breadth First Search(BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is______ .

16 | |

15 | |

31 | |

32 |

Question 6 Explanation:

Question 7 |

Consider the following directed graph:

The number of different topological orderings of the vertices of the graph is

The number of different topological orderings of the vertices of the graph is

4 | |

5 | |

6 | |

7 |

Question 7 Explanation:

Question 8 |

Let G = (V, E) be a simple undirected graph, and s be a particular vertex in it called the source. For x \in V, let d(x) denote the shortest distance in G from s to x. A breadth first search (BFS) is performed starting at s. Let T be the resultant BFS tree. If (u,v) is an edge of G that is not in T, then which one of the following CANNOT be the value of d(u)-d(v)?

-1 | |

0 | |

1 | |

2 |

Question 8 Explanation:

Question 9 |

Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _________.

16 | |

19 | |

17 | |

20 |

Question 9 Explanation:

Question 10 |

Let G be a graph with n vertices and m edges. What is the tightest upper bound on the
running time of Depth First Search on G, when G is represented as an adjacency matrix?

\Theta (n) | |

\Theta (n+m) | |

\Theta (n^{2}) | |

\Theta (m^{2}) |

Question 10 Explanation:

There are 10 questions to complete.