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Quiz Chapter 5: Network Theory

10 questions · Form 4 Mathematics Bab 5: Network Theory

Question 1 of 10Score: 0

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

Full Question List & Answer Key

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

1. 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.

2. 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.

3. What is a weighted graph?

  1. A. A graph where edges carry arrows showing direction
  2. B. A graph with numerical values assigned to its edges representing distance, time, or cost
  3. C. A graph where all vertices have equal degrees
  4. D. A tree that contains all vertices of a original graph
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Answer: B

A weighted graph is a graph in which each edge is assigned a numerical weight representing quantities like cost, time, or distance.

4. 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.

5. 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.

6. 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.

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. 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.

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. 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.

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