Test Series - Data Structure

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Test Number 108/115

Q: 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
Solution: In a walk if the vertices are distinct it is called a path, whereas if the edges are distinct it is called a trail.
Q: 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
Solution: Number of ways in which every vertex can be connected to each other is nC2.
Q: A connected planar graph having 6 vertices, 7 edges contains _____________ regions.
A. 15
B. 3
C. 1
D. 11
Solution: By euler’s formula the relation between vertices(n), edges(q) and regions(r) is given by n-q+r=2.
Q: 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
Solution: A simple graph maybe connected or disconnected.
Q:  What is the maximum number of edges in a bipartite graph having 10 vertices?
A. 24
B. 21
C. 25
D. 16
Solution: 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.
Q: 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
Solution: A graph must contain at least one vertex.
Q: 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. v = e-1
Solution: For any connected graph with no cycles the equation holds true.
Q: A graph with all vertices having equal degree is known as a __________
A. Multi Graph
B. Regular Graph
C. Simple Graph
D. Complete Graph
Solution: The given statement is the definition of regular graphs.
Q: 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. No way to represent
Solution: Adjacency Matrix, Adjacency List and Incidence Matrix are used to represent a graph.

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