## Graph MCQ

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

View Answer

Ans : B

Explanation: Number of ways in which every vertex can be connected to each other is nC2.

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

View Answer

Ans : B

Explanation: The sum of the degrees of the vertices is equal to twice the number of edges.

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

View Answer

Ans : A

Explanation: The union of G and G’ would be a complete graph so, the number of edges in G’= number of edges in the complete form of G(nC2)-edges in G(m).

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

View Answer

Ans : A

Explanation: A simple graph maybe connected or disconnected.

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

View Answer

Ans : B

Explanation: A graph must contain at least one vertex.

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

View Answer

Ans : B

Explanation: For any connected graph with no cycles the equation holds true.

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

View Answer

Ans : A

Explanation: A graph is eulerian if either all of its vertices are even or if only two of its vertices are odd.

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

View Answer

Ans : B

Explanation: The given statement is the definition of regular graphs.Explanation: The given statement is the definition of regular graphs.

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

A. Adjacency List and Adjacency Matrix

B. Incidence Matrix

C. Adjacency List, Adjacency Matrix as well as Incidence Matrix

D. None of the mentioned

View Answer

Ans :C

Explanation: The 3 listed methods can be used, the choice depends on the ease of use.

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)

View Answer

Ans : D

Explanation: As V entries are 0, a total of V2-V entries are to be examined.

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