This set of Data Structure Multiple Choice Questions & Answers (MCQs) focuses 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
Explanation: In a walk if the vertices are distinct it is called a path, whereas if the edges are distinct it is called a trail.
Explanation: 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
Explanation: 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?
d) Information given is insufficient
Explanation: Number of ways in which every vertex can be connected to each other is nC2.
Explanation: 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.
Explanation: 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.
Explanation: 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 ___________
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).
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
Explanation: A simple graph maybe connected or disconnected.
10. What is the maximum number of edges in a bipartite graph having 10 vertices?
Explanation: 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
Explanation: A graph must contain at least one vertex.
12. 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?
b) v = e+1
c) v + 1 = e
d) v = e-1
Explanation: For any connected graph with no cycles the equation holds true.
13. For which of the following combinations of the degrees of vertices would the connected graph be eulerian?
Explanation: A graph is eulerian if either all of its vertices are even or if only two of its vertices are odd.
14. A graph with all vertices having equal degree is known as a __________
a) Multi Graph
b) Regular Graph
c) Simple Graph
d) Complete Graph
Explanation: The given statement is the definition of regular graphs.
15. 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
Explanation: Adjacency Matrix, Adjacency List and Incidence Matrix are used to represent a graph.
Sanfoundry Global Education & Learning Series – Data Structure.
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