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# Data Structure MCQ - Graph

This section focuses on the "Graph" of the Data Structure. These Multiple Choice Questions (mcq) should be practiced to improve the Data Structure skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

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

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)

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.
D. All of the above

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

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

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

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

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

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

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

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

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)

11. What is the number of edges present in a complete graph having n vertices?

A. (n*(n+1))/2
B. (n*(n-1))/2
C. n
D. Information given is insufficient

12. In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices.

A. True
B. False

13. If a simple graph G, contains n vertices and m edges, the number of edges in the Graph G'(Complement of G) is ___________

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

14. Which of the following properties does a simple graph not hold?

A. Must be connected
B. Must be unweighted
C. Must have no loops or multiple edges
D. All of the mentioned

15. Which of the following is true?

A. A graph may contain no edges and many vertices
B. A graph may contain many edges and no vertices
C. A graph may contain no edges and no vertices
D. None of the mentioned

16. For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?

A. v=e
B. v = e+1
C. v + 1 = e
D. None of the mentioned

17. for which of the following combinations of the degrees of vertices would the connected graph be eulerian?

A. 1,2,3
B. 2,3,4
C. 2,4,5
D. 1,3,5

18. A graph with all vertices having equal degree is known as a __________

A. Multi Graph
B. Regular Graph
C. Simple Graph
D. Complete Graph

19. Which of the following ways can be used to represent a graph?

B. Incidence Matrix
D. None of the mentioned

20. The time complexity to calculate the number of edges in a graph whose information in stored in form of an adjacency matrix is ____________

A. O(V)
B. O(E2)
C. O(E)
D. O(V2)

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