Question 1 |

Let U = \{1, 2, 3\}. Let 2^U denote the powerset of U. Consider an undirected graph
G whose vertex set is 2^U. For any A,B \in 2^U, (A,B) is an edge in G if and only
if (i) A \neq B, and (ii) either A \subseteq B or B \subseteq A. For any vertex A in G, the set of
all possible orderings in which the vertices of G can be visited in a Breadth First
Search (BFS) starting from A is denoted by B(A).

If \phi denotes the empty set, then the cardinality of B(\phi ) is ____.

If \phi denotes the empty set, then the cardinality of B(\phi ) is ____.

524 | |

63218 | |

5040 | |

2540 |

Question 1 Explanation:

Question 2 |

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 2 Explanation:

Question 3 |

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 3 Explanation:

Question 4 |

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 4 Explanation:

Question 5 |

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 5 Explanation:

There are 5 questions to complete.