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Quiz Chapter 5: Network Theory

10 questions · Form 4 Mathematics Bab 5: Network Theory

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. How many degree count contributions does a single loop at a vertex add to that vertex?

  1. A. 0
  2. B. 1
  3. C. 2
  4. D. 4
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Answer: C

A loop connects a vertex to itself and both ends touch the vertex, adding 2 to the degree count of that vertex.

2. Given that the sum of degrees of a graph is 18, calculate the number of edges in the graph.

  1. A. 6
  2. B. 9
  3. C. 18
  4. D. 36
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Answer: B

Using sum d(v) = 2E: 18 = 2E, which gives E = 182 = 9 edges.

3. A subgraph G' = (V', E') of G = (V, E) must satisfy which conditions?

  1. A. V' is a subset of V and E' is a subset of E
  2. B. V' is equal to E' and V is equal to E
  3. C. V' has more elements than V
  4. D. E' contains edges between vertices not in V'
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Answer: A

By definition, a subgraph G' contains a subset of vertices V' ⊆ V and a subset of edges E' ⊆ E from the main graph G.

4. What is the total sum of degrees for a graph with vertices V = {A, B, C, D} and degree of vertices d(A)=3, d(B)=2, d(C)=4, d(D)=3?

  1. A. 6
  2. B. 10
  3. C. 12
  4. D. 24
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Answer: C

Sum of degrees = d(A) + d(B) + d(C) + d(D) = 3 + 2 + 4 + 3 = 12.

5. If a tree has 9 vertices, how many edges must it have?

  1. A. 8
  2. B. 9
  3. C. 10
  4. D. 18
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Answer: A

In any tree, the relation between vertices (V) and edges (E) is given by E = V - 1. So E = 9 - 1 = 8.

6. Given a simple graph with 5 vertices. What is the maximum possible number of edges it can have?

  1. A. 5
  2. B. 8
  3. C. 10
  4. D. 20
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Answer: C

The maximum number of edges in a simple graph with n vertices is nn - 12. For n = 5, maximum edges = 542 = 10.

7. Given set V = {1, 2, 3, 4} and set E = {(1, 2), (1, 3), (2, 3), (3, 4)}. What is the degree of vertex 3?

  1. A. 1
  2. B. 2
  3. C. 3
  4. D. 4
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Answer: C

Vertex 3 appears in three edge pairs: (1, 3), (2, 3), and (3, 4). Therefore, its degree is 3.

8. Which statement is true regarding the sum of in-degrees and out-degrees in a directed graph?

  1. A. Sum of in-degrees > Sum of out-degrees
  2. B. Sum of in-degrees < Sum of out-degrees
  3. C. Sum of in-degrees = Sum of out-degrees = Total edges E
  4. D. Sum of in-degrees = 2 × Total edges E
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Answer: C

Every directed edge originates from one vertex (out-degree) and ends at another (in-degree). Thus, sum d_in(v) = sum d_out(v) = E.

9. In a directed graph, if a vertex has an in-degree of 3 and an out-degree of 2, what is its total degree?

  1. A. 1
  2. B. 5
  3. C. 6
  4. D. 8
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Answer: B

Total degree of a vertex in a directed graph is the sum of its in-degree and out-degree: 3 + 2 = 5.

10. Can a graph have a sum of degrees equal to 15?

  1. A. Yes, for any graph with odd vertices
  2. B. Yes, if it is a directed graph
  3. C. No, because the sum of degrees must always be an even number
  4. D. No, because edges cannot be connected to odd vertices
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Answer: C

Since sum d(v) = 2E and E is an integer, the sum of degrees must always be an even integer. 15 is odd, so it is impossible.

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