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# Discrete Mathematics | Week 7

## Quiz

1. Which of the following graphs are not complete graphs?

Explanation

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

c. ⟨4,4,3,3,3,5,2⟩

Explanation

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

c.  (𝐵, 𝐸) and 𝐸

Explanation

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

d.  1,1

Explanation

5. Which of the following is a graphic sequence?

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

Explanation

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

a. {𝐴 − 𝐵 − 𝐸 − 𝐹 − 𝐺 − 𝐻}

d. {𝐴 − 𝐹 − 𝐶 − 𝐵 − 𝐸 − 𝐷 − 𝐶 − 𝐻}

f. {𝐴 − 𝐻}

Explanation

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

b. False

Explanation

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?

a. 1

Explanation

9. Observe the following graph.

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

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

Explanation

10. 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.

d. I and II

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