Discrete Mathematics Week 7 NPTEL

                     

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.

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

b.

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

c.

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

d.

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

e.

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

f.

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

g.

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

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?

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

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?

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

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)

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

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)

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

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