Correct Answer :

2. What is the degree sequence of the given graph?

• • • • ⟨4,3,3,3,3,5,2⟩

      • ⟨4,4,3,3,3,4,2⟩

      • ⟨4,4,3,3,3,5,2⟩

      • ⟨4,3,3,3,3,4,2⟩

Correct Answer : ⟨4,4,3,3,3,5,2⟩

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

• (𝐵, 𝐷) and 𝐵

• (𝐸,𝐹) and 𝐹

• (𝐵, 𝐸) and 𝐸

• (𝐴,𝐵) and 𝐴

Correct Answer : (𝐵, 𝐸) and 𝐸

4. The number of components in a 𝐾𝑛 and 𝐶n respectively are?

• • • • 2,2

      • 2,1

      • 1,2

      • 1,1

Correct Answer : 1,1

5. Which of the following is a graphic sequence?

• • • • 5,3,3,2,2,1

      • 2,1,1,1,1,1

      • 6,5,4,3,2,1

      • 5,5,2,2,1,1

Correct Answer : 5,5,2,2,1,1

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

• {𝐴 − 𝐵 − 𝐸 − 𝐹 − 𝐺 − 𝐻}

• {𝐴 − 𝐵 − 𝐶 − 𝐻}

• {𝐴 − 𝐹 − 𝐸 − 𝐵 − 𝐶 − 𝐻}

• {𝐴 − 𝐹 − 𝐶 − 𝐵 − 𝐸 − 𝐷 − 𝐶 − 𝐻}

• {𝐴 − 𝐹 − 𝐸 − 𝐷 − 𝐶 − 𝐻}

• {𝐴 − 𝐻}

• {𝐴 − 𝐹 − 𝐸 − 𝐻}

• {𝐴 − 𝐵 − 𝐶 − 𝐷 − 𝐸 − 𝐻}

Correct Answer : {𝐴 − 𝐵 − 𝐸 − 𝐹 − 𝐺 − 𝐻}

{𝐴 − 𝐻}

7. If an edge is removed from a cycle in a graph, then the graph becomes disconnected.

State whether true/false.

• True

• False

Correct Answer : False

8. 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?

• 1

• More than 1

• 0

• 𝑛 – 1

Correct Answer : 1

9. Observe the following graph. (MSQ)

Choose the correct option(s) from below.

• {𝐷 − 𝐸 − 𝐹 − 𝐺 − 𝐶 − 𝐷} is a cycle

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

• {𝐴 − 𝐵 − 𝐷 − 𝐴} is a not cycle

• {𝐴 − 𝐵 − 𝐷 − 𝐶 − 𝐷 − 𝐹} is a trail

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

Correct Answer :{𝐷 − 𝐸 − 𝐹 − 𝐺 − 𝐶 − 𝐷} is a cycle

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

10. Which o f 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.

• • • Only I

    • Only II

    • Only III

    • I and II

    • I and III

    • I, II and III

Correct Answer : I and II

WEEK-7 DETAILED SOLUTION