# Discrete Mathematics Week 7 NPTEL

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

Course name: Discrete Mathematics

Check and submit Discrete Mathematics Week 7 NPTEL assignment here

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

b.

c.

d.

e.

f.

g.

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⟩

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

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

Keep visiting for further changes

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}

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

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

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.

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