Top MCQs on Graph Traversals with Answers

Question 11

Is the following statement true/false? A DFS of a directed graph always produces the same number of tree edges, i.e., independent of the order in which vertices are considered for DFS. 

• True

• False

Question 12

If the DFS finishing time f[u] > f[v] for two vertices u and v in a directed graph G, and u and v are in the same DFS tree in the DFS forest, then u is an ancestor of v in the depth-first tree.

• True

• False

Question 13

Consider the DAG with Consider V = {1, 2, 3, 4, 5, 6}, shown below. Which of the following is NOT a topological ordering? 

[caption width="800"] [/caption]

• 1 2 3 4 5 6

• 1 3 2 4 5 6

• 1 3 2 4 6 5

• 3 2 4 1 6 5

Question 14

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

• O(n)
• O(m+n)
• O(n²)
• O(mn)

Question 15

Consider the tree arcs of a BFS traversal from a source node W in an unweighted, connected, undirected graph. The tree T formed by the tree arcs is a data structure for computing.

• the shortest path between every pair of vertices.

• the shortest path from W to every vertex in the graph.

• the shortest paths from W to only those nodes that are leaves of T.

• the longest path in the graph

Question 16

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 _________.

• 17
• 18
• 19
• 20

Question 17

Let T be a depth first search tree in an undirected graph G. Vertices u and n are leaves of this tree T. The degrees of both u and n in G are at least 2. which one of the following statements is true?

• There must exist a vertex w adjacent to both u and n in G
• There must exist a vertex w whose removal disconnects u and n in G
• There must exist a cycle in G containing u and n
• There must exist a cycle in G containing u and all its neighbours in G.

Question 18

Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?

• {u,v} must be an edge in G, and u is a descendant of v in T
• {u,v} must be an edge in G, and v is a descendant of u in T
• If {u,v} is not an edge in G then u is a leaf in T
• If {u,v} is not an edge in G then u and v must have the same parent in T

Question 19

In a depth-first traversal of a graph G with n vertices, k edges are marked as tree edges. The number of connected components in G is

• k
• k + 1
• n - k - 1
• n - k

Question 20

Consider the following directed graph. The number of different topological orderings of the vertices of the graph is   Note : This question was asked as Numerical Answer Type.

• 1

• 2

• 4

• 6