# Discrete Mathematics Week 8 NPTEL

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

**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

**Answer: 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

**Answer: c, d**

**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

**Answer: a. 12**

**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. k_{6}

**Answer: a, d**

**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 G _{C} , where G has 12 vertices and 34 edges.**

a. 66

b. 32

c. 33

d. 34

**Answer: b. 32**

**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

**Answer: d. 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

**Answer: c. Hamiltonian 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

**Answer: 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

**Answer: c. 0**

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

a. 4,3

b. 4,4

c. 2,3

d. 3,3

**Answer: d. 3,3**

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

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