Graph MCQ

1. Which of the following statements for a simple graph is correct?

A. Every path is a trail
B. Every trail is a path
C. Every trail is a path as well as every path is a trail
D. None of the mentioned

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2. What is the maximum number of possible non zero values in an adjacency matrix of a simple graph with n vertices?

A. (n*(n-1))/2
B. (n*(n+1))/2
C. n*(n-1)
D. n*(n+1)

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3. Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph?

A. In adjacency list representation, space is saved for sparse graphs.
B. DFS and BSF can be done in O(V + E) time for adjacency list representation. These operations take O(V^2) time in adjacency matrix representation. Here is V and E are number of vertices and edges respectively.
C. Adding a vertex in adjacency list representation is easier than adjacency matrix representation.
D. All of the above

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4.A connected planar graph having 6 vertices, 7 edges contains _____________ regions.

A. 15
B. 3
C. 1
D. 11

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5.On which of the following statements does the time complexity of checking if an edge exists between two particular vertices is not, depends?

A. Depends on the number of edges
B. Depends on the number of vertices
C. Is independent of both the number of edges and vertices
D. It depends on both the number of edges and vertices

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6. The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
   I. 7, 6, 5, 4, 4, 3, 2, 1
   II. 6, 6, 6, 6, 3, 3, 2, 2
   III. 7, 6, 6, 4, 4, 3, 2, 2
   IV. 8, 7, 7, 6, 4, 2, 1, 1

A. I and II
B. III and IV
C. IV only
D. II and IV

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7. What is the maximum number of edges in a bipartite graph having 10 vertices?

A. 24
B. 21
C. 25
D. 16

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8. Possible number of labelled simple Directed, Pseudo and Multigarphs exist having 2 vertices?

A. 3, Infinite, 4
B. 4, 3, Infinite
C. 4, Infinite, infinite
D. 4, Infinite, Infinite

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9.The most efficient algorithm for finding the number of connected components in an undirected graph on n vertices and m edges has time complexity.
   (A)   \theta(n)
   (B)   \theta(m)
   (C)   \theta(m + n)
   (D)   \theta(mn)

A. A
B. B
C. C
D. D

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10. What is time complexity to check if a string(length S1) is a substring of another string(length S2) stored in a Directed Acyclic Word Graph, given S2 is greater than S1?

A. O(S1)
B. O(S2)
C. O(S1+S2)
D. O(1)

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