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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. 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.

2. 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.

3. 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.

4. 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.

5. A connected graph has 6 vertices and 5 edges without any loops or multiple edges. What type of graph is it?

  1. A. Directed graph
  2. B. Complete graph
  3. C. Tree
  4. D. Weighted loop graph
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Answer: C

A connected simple graph with V vertices and E = V - 1 edges (here E = 6 - 1 = 5) is a tree.

6. In a transportation network graph, what do weighted edges usually represent?

  1. A. Names of cities
  2. B. Traffic lights
  3. C. Travel distance, time, or fuel cost
  4. D. Vehicle registration numbers
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Answer: C

Weights in transportation networks denote physical quantities between nodes, such as travel distance, duration, or cost.

7. What is the minimum total weight of a minimum spanning tree for a complete graph with 3 vertices A, B, C where edge weights are AB = 3, BC = 4, AC = 5?

  1. A. 7
  2. B. 8
  3. C. 9
  4. D. 12
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Answer: A

For 3 vertices, a tree needs V - 1 = 2 edges. To minimize weight, select the 2 smallest edges: 3 (AB) and 4 (BC). Total = 3 + 4 = 7.

8. 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.

9. 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.

10. If a graph has 4 vertices with degrees 1, 2, 3, and 2 respectively, how many edges does it contain?

  1. A. 4
  2. B. 8
  3. C. 12
  4. D. 16
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Answer: A

Sum of degrees = 1 + 2 + 3 + 2 = 8. Using sum d(v) = 2E: 8 = 2E, so E = 4.

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