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# Graph Theory MCQ Questions - Discrete Mathematics

This section focuses on "Graph" in Discrete Mathematics. These Multiple Choice Questions (mcq) should be practiced to improve the Discrete Mathematics skills required for various interviews (campus interviews, walk-in interviews, company interviews), placements, entrance exams and other competitive examinations.

1. A graph is a set of points, called?

A. Nodes
B. Edge
C. fields
D. lines

2. Graph consists of a?

A. non-empty set of vertices
B. empty set of vertices
C. Both A and B
D. None of the above

3. Number of edges incident with the vertex V is called?

A. Degree of a Graph
B. Handshaking Lemma
C. Degree of a Vertex
D. None of the above

4. Which of the following is true about Handshaking Lemma?

A. In Handshaking lemma, If the degree of a vertex is even, the vertex is called an even vertex
B. The degree of a graph is the largest vertex degree of that graph.
C. The degree of a vertex is odd, the vertex is called an odd vertex.
D. The sum of all the degrees of all the vertices is equal to twice the number of edges.

5. What is Null Graph?

A. A null graph has no nodes
B. null graph has no edges
C. null graph has no odd vertex
D. null graph has no even vertex

6. If in a graph multiple edges between the same set of vertices are allowed, it is called?

A. Hamiltonian Graphs
B. Simple graph
C. Multi graph
D. Euler Graphs

7. The graph in which, there is a closed trail which includes every edge of the graph is known as?

A. Hamiltonian Graphs
B. Euler Graphs
C. Planar graph
D. Directed Graph

8. In a 7-node directed cyclic graph, the number of Hamiltonian cycle is to be

A. 180
B. 720
C. 360
D. 540

9. If G is the forest with 54 vertices and 17 connected components, G has _______ total number of edges.

A. 35
B. 36
C. 37
D. 38

10. Triangle free graphs have the property of clique number is __________

A. More than 10
B. less than 5
C. equal to 5
D. greater than 3