Lesson DB1-DB3

DB1-DB3 Network language, spanning trees and route inspection Quiz: AQA Further Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson DB1-DB3, Network language, spanning trees and route inspection: 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. What does a weight on a network arc typically represent?

    • Node degree
    • Flow rate
    • Vertex capacity
    • Cost or distance

  2. In network theory, what is a line connecting two nodes called?

    • A path
    • An arc
    • A degree
    • A tree

  3. How many arcs does a spanning tree of a network with n nodes contain?

    • n
    • n - 1
    • 2n - 1
    • n + 1

  4. How does Kruskal's algorithm select arcs for a minimum spanning tree?

    • Lowest weight first
    • Highest weight first
    • From a start node
    • By random selection

  5. A network has the arcs AB = 2, BC = 3, CD = 4, DA = 5 and AC = 6, with nodes A, B, C and D. What is the weight of a minimum spanning tree?

    • 20
    • 10
    • 14
    • 9

  6. A connected network has every node of even degree and total arc weight 30. What is the minimum length of a route that traverses every arc at least once and returns to its start?

    • 30
    • 60
    • 32
    • 28

  7. The network with arcs AB = 2, BC = 3, CD = 4, DA = 5 and AC = 6 has odd-degree nodes A and C. What is the minimum length of a route inspecting every arc, to the nearest integer?

    • 26
    • 20
    • 30
    • 25

  8. In a route inspection problem, a network has four odd-degree nodes. How many different ways are there to pair these four odd nodes?

    • 2
    • 4
    • 3
    • 6

  9. A minimum spanning tree is built by Prim's algorithm starting at node A in the network with arcs AB = 2, BC = 3, CD = 4, DA = 5 and AC = 6. Which arc is added first?

    • DA
    • CD
    • AC
    • AB

  10. A network has 7 nodes and 10 arcs. How many arcs must be removed to leave a spanning tree?

    • 6
    • 3
    • 7
    • 4

  11. A network has arcs PQ = 4, PR = 1, QR = 3, RS = 2 and QS = 5, with nodes P, Q, R and S. What is the weight of a minimum spanning tree?

    • 8
    • 10
    • 7
    • 6

  12. A route inspection problem has odd-degree nodes X and Y, a shortest path between X and Y of weight 7, and total arc weight 40. What is the minimum length of the route?

    • 33
    • 54
    • 47
    • 40

  13. What is the objective of the route inspection problem?

    • Shortest simple tree
    • Maximum-weight path
    • Minimum-weight closed walk
    • Minimum vertex cover

  14. What does the degree of a node in a network measure?

    • Arc weight sum
    • Connected arcs
    • Node capacity
    • Shortest path

  15. A network has 5 nodes. How many arcs does every spanning tree of the network have?

    • 3
    • 5
    • 6
    • 4

  16. Why must arcs be repeated in route inspection on networks with odd nodes?

    • To make nodes even
    • To create a tree
    • To remove loops
    • To increase total weight

  17. What does a minimum spanning tree minimise for a network?

    • Shortest path distance
    • Maximum vertex degree
    • Number of cycles
    • Total arc weight

  18. A network has arcs AB = 3, AC = 1, BC = 2, BD = 4 and CD = 5. What is the weight of a minimum spanning tree?

    • 10
    • 8
    • 7
    • 12

  19. Which arcs are repeated in the optimal route inspection for a network with two odd nodes P and Q?

    • The longest arc
    • All adjacent arcs
    • Arcs incident to P
    • Shortest path P to Q

  20. How does the weight of a minimum spanning tree compare to any other spanning tree?

    • Less than or equal
    • Strictly less than
    • Always equal
    • Greater than or equal

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