# Discrete Mathematics Week 7 NPTEL

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

Course name: Discrete Mathematics

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**Q1. Which of the following graphs are not complete graphs? (MSQ)**

a.

b.

c.

d.

e.

f.

g.

**Answer: b, e**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

**Q2. What is the degree sequence of the given graph?**

a. ⟨4,3,3,3,3,5,2⟩

b. ⟨4,4,3,3,3,4,2⟩

c. ⟨4,4,3,3,3,5,2⟩

d. ⟨4,3,3,3,3,4,2⟩

**Answer: c. ⟨4,4,3,3,3,5,2⟩**

**Q3. What are the cut edge and the cut vertex respectively, in the following graph?**

a. (𝐵, 𝐷) and 𝐵

b. (𝐸,𝐹) and 𝐹

c. (𝐵, 𝐸) and 𝐸

d. (𝐴,𝐵) and 𝐴

**Answer: c. (𝐵, 𝐸) and 𝐸**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

**Q4. The number of components in a Kn𝐾𝑛 andCn𝐶n respectively are?**

a. 2,2

b. 2,1

c. 1,2

d. 1,1

**Answer: d. 1,1**

**Q5. Which of the following is a graphic sequence?**

a. 5,3,3,2,2,1

b. 2,1,1,1,1,1

c. 6,5,4,3,2,1

d. 5,5,2,2,1,1

**Answer: a. 5,3,3,2,2,1**

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**Q6. Which of the following is not a path from A to H? (MSQ)**

a. {𝐴 − 𝐵 − 𝐸 − 𝐹 − 𝐺 − 𝐻}

b. {𝐴 − 𝐵 − 𝐶 − 𝐻}

c. {𝐴 − 𝐹 − 𝐸 − 𝐵 − 𝐶 − 𝐻}

d. {𝐴 − 𝐹 − 𝐶 − 𝐵 − 𝐸 − 𝐷 − 𝐶 − 𝐻}

e. {𝐴 − 𝐹 − 𝐸 − 𝐷 − 𝐶 − 𝐻}

f. {𝐴 − 𝐻}

g. {𝐴 − 𝐹 − 𝐸 − 𝐻}

h. {𝐴 − 𝐵 − 𝐶 − 𝐷 − 𝐸 − 𝐻}

**Answer: a, d, f**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

**Q7. If an edge is removed from a cycle in a graph, then the graph becomes disconnected.State whether true/false.**

a. True

b. False

**Answer: b. False**

**Q8. For a simple graph with vertices, how many subgraphs can be constructed, such that the subgraph is an induced subgraph as well as a spanning subgraph?**

a. 1

b. More than 1

c. 0

d. 𝑛 – 1

**Answer: a. 1**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

**Q9. Observe the following graph. (MSQ)**

**Choose the correct option(s) from below.**

a. {𝐷 − 𝐸 − 𝐹 − 𝐺 − 𝐶 − 𝐷} is a cycle

b. {𝐻 − 𝐵 − 𝐷 − 𝐶 − 𝐺 − 𝐹 − 𝐷 − 𝐴} is a trail

c. {𝐴 − 𝐵 − 𝐷 − 𝐴} is a not cycle

d. {𝐴 − 𝐵 − 𝐷 − 𝐶 − 𝐷 − 𝐹} is a trail

e. {𝐴 − 𝐵 − 𝐷 − 𝐶 − 𝐺 − 𝐹 − 𝐷 − 𝐴} is a circuit.

**Answer: a, b, e**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

**Q10. Which of the following statements is/are true? I) If there is a walk from P to Q then, there must be a path from P to Q. II) The number of edges in a tree is equal to one less than the number of vertices.III) Every graph has an odd number of odd–degree vertices**.

a. Only I

b. Only II

c. Only III

d. I and II

e. I and III

f. I, II and III

**Answer: d. I and II**

**These are the solution of Discrete Mathematics Week 7 NPTEL Assignment 7 Solution Answers**

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