Lesson DA4-DA5

DA4-DA5 Planarity, complete and bipartite graphs Quiz: AQA Further Maths, Unit 5

20 questions

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Lesson DA4-DA5, Planarity, complete and bipartite graphs: 20 multiple choice questions for the AQA Further Maths (7367), Unit 5: Optional application 3: discrete mathematics, written with Revision Ninja.

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The 20 questions

  1. According to Kuratowski's theorem, a graph is non-planar if it contains a subdivision of which graphs?

    • K4 or K2,3
    • K3 or K2,2
    • K6 or K4,4
    • K5 or K3,3
  2. In a complete graph Kn, how many edges connect each pair of distinct vertices?

    • Exactly one
    • Exactly two
    • At least one
    • Zero
  3. In a bipartite graph, between which sets of vertices can edges exist?

    • Any arbitrary sets
    • The same set
    • Two disjoint sets
    • Three disjoint sets
  4. Which edges are included in the complement of a simple graph G?

    • Edges forming cycles
    • All possible edges
    • Connected vertex pairs
    • Unconnected vertex pairs
  5. How many edges does the complete graph K7 have?

    • 49
    • 21
    • 42
    • 14
  6. How many edges does the complete bipartite graph K3,4 have?

    • 6
    • 12
    • 7
    • 24
  7. The complete bipartite graph K3,3 has 6 vertices. How many edges does its complement have?

    • 3
    • 12
    • 9
    • 6
  8. What is the maximum number of edges a simple planar graph with 6 vertices can have?

    • 9
    • 10
    • 12
    • 15
  9. What is the maximum number of edges a simple bipartite planar graph with 6 vertices can have?

    • 6
    • 9
    • 8
    • 12
  10. Which of the following graphs is non-planar according to Kuratowski's theorem?

    • K2,4
    • K3,3
    • K4
    • K2,3
  11. A simple graph has 5 edges. What is the sum of all the entries in its adjacency matrix?

    • 25
    • 20
    • 5
    • 10
  12. In an adjacency matrix of a simple graph, what does a row sum represent?

    • Chromatic number
    • Number of paths
    • Total edge count
    • Vertex degree
  13. Can a graph containing a cycle of odd length be bipartite?

    • Never
    • Only if connected
    • Always
    • Only if complete
  14. What maximum number of edges can a simple planar graph with 5 vertices have?

    • 10
    • 9
    • 12
    • 8
  15. What is the planarity status of the complete bipartite graph K2,3?

    • Planar
    • Hamiltonian
    • Semi-planar
    • Non-planar
  16. For which smallest value of n does the complete graph Kn break the planar edge bound e ≤ 3n - 6?

    • 3
    • 4
    • 6
    • 5
  17. What maximum number of edges can a simple planar graph with 7 vertices have?

    • 14
    • 15
    • 21
    • 16
  18. What maximum number of edges can a simple planar bipartite graph with 10 vertices have?

    • 20
    • 24
    • 16
    • 26
  19. According to Kuratowski's theorem, a graph is non-planar if it contains a subdivision of which graph?

    • K3,3 or K4,4
    • K5 or K3,3
    • K5 or K4,4
    • K4 or K2,3
  20. How many entries equal 1 in the adjacency matrix of the complete graph K4?

    • 4
    • 16
    • 12
    • 6

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