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.