Data Structure Multiple Choice Questions on “Graph”.
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) Path and trail have no relation
Answer: a
Clarification: In a walk if the vertices are distinct it is called a path, whereas if the edges are distinct it is called a trail.
2. In the given graph identify the cut vertices.
a) B and E
b) C and D
c) A and E
d) C and B
Answer: d
Clarification: After removing either B or C, the graph becomes disconnected.
3. For the given graph(G), which of the following statements is true?
a) G is a complete graph
b) G is not a connected graph
c) The vertex connectivity of the graph is 2
d) The edge connectivity of the graph is 1
Answer: c
Clarification: After removing vertices B and C, the graph becomes disconnected.
4. 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
Answer: b
Clarification: Number of ways in which every vertex can be connected to each other is nC2.
5. The given Graph is regular.
a) True
b) False
Answer: a
Clarification: In a regular graph, degrees of all the vertices are equal. In the given graph the degree of every vertex is 3.
6. In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices.
a) True
b) False
Answer: b
Clarification: The sum of the degrees of the vertices is equal to twice the number of edges.
7. A connected planar graph having 6 vertices, 7 edges contains _____________ regions.
a) 15
b) 3
c) 1
d) 11
Answer: b
Clarification: By euler’s formula the relation between vertices(n), edges(q) and regions(r) is given by n-q+r=2.
8. 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
Answer: a
Clarification: 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).
9. 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) Must have no multiple edges
Answer: a
Clarification: A simple graph maybe connected or disconnected.
10. What is the maximum number of edges in a bipartite graph having 10 vertices?
a) 24
b) 21
c) 25
d) 16
Answer: c
Clarification: Let one set have n vertices another set would contain 10-n vertices.
Total number of edges would be n*(10-n), differentiating with respect to n, would yield the answer.
11. 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) A graph may contain no vertices and many edges