# Discrete Mathematics Week 8 NPTEL

### These are the solution of Discrete Mathematics Week 8 NPTEL Assignment 8 Solution Answers

Course name: Discrete Mathematics

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Q1. What is the number of colors required to color a complete graph containing n vertices?
a. 3
b. 4
c. n/(n−1)
d. n

Q2. Which of the following graphs does not have an Eulerian circuit?
a. A complete graph with 79 vertices
b.

c.

d. Complement of the graph

These are the solution of Discrete Mathematics Week 8 NPTEL Assignment 8 Solution Answers

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Q3. What is the number of edges for a connected planar graph having 8 vertices, and 6 regions?
a. 12
b. 14
c. 8
d. 10

Q4. Which of the following graphs can be concluded to be Hamiltonian?
a. A graph with the number of edges of every node, greater than n/2.
b.

c.

d. k6

These are the solution of Discrete Mathematics Week 8 NPTEL Assignment 8 Solution Answers

Q5. Find the total number of edges in the complement graph GC , where G has 12 vertices and 34 edges.
a. 66
b. 32
c. 33
d. 34

Q6. Which of the following statement(s) is/are true?
I) We can find a tree that is not planar.
II) We can conclude that a graph is connected if the degree of all the vertices is greater than equal to n/2.
III) Given a graph G, there is a cycle of length k and k is less than equal to n, then we can find a path of length at least k+1.

a. Only I
b. Only III
c. I and II
d. II and III
e. I II and III

Q7. A graph where we can traverse through all the vertices, without repeating edges or vertices more than once is called?
a. Planar graph
b. Complete graph
c. Hamiltonian graph
d. Eulerian graph

These are the solution of Discrete Mathematics Week 8 NPTEL Assignment 8 Solution Answers

Q8. State whether true/false: A bipartite graph can have an odd cycle.
a. True
b. False

Q9. What is the cardinality of the set of edges of the complement of a complete graph G having 5 vertices?
a. 10
b. 5
c. 0
d. 2

Q10. What is the chromatic number of the graph given below respectively?

a. 4,3
b. 4,4
c. 2,3
d. 3,3