arrow_backBack to Study Resources

Quiz Chapter 5: Network Theory

10 questions · Form 4 Mathematics Bab 5: Network Theory

Question 1 of 10Score: 0

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

Full Question List & Answer Key

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

1. 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'
Show answer

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.

2. Which of the following is NOT a property of a tree in graph theory?

  1. A. It is a connected graph.
  2. B. It contains no loops.
  3. C. It contains no multiple edges.
  4. D. It contains closed circuits or cycles.
Show answer

Answer: D

A tree must be connected and acyclic (contains no closed loops, cycles, or circuits).

3. In social network analysis represented by a graph, what do the vertices usually represent?

  1. A. Interactions or messages sent
  2. B. Individuals or people
  3. C. Distance between houses
  4. D. Internet server bandwidths
Show answer

Answer: B

In social network graphs, vertices represent entities or individuals, while edges represent relationships or interactions.

4. 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
Show answer

Answer: C

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

5. 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
Show answer

Answer: B

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

6. 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
Show answer

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.

7. 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
Show answer

Answer: A

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

8. 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
Show answer

Answer: C

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

9. 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
Show answer

Answer: C

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

10. 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
Show answer

Answer: B

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

Sponsored