MCQ - Graph in Data Structure

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

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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

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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

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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

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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

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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

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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

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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

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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

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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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