Lesson DA6-DA7

DA6-DA7 Trees and isomorphism of graphs Quiz: AQA Further Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson DA6-DA7, Trees and isomorphism of 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. In graph theory, how is a tree defined?

    • Connected acyclic graph
    • Disconnected acyclic graph
    • Connected cyclic graph
    • Complete bipartite graph

  2. What features are completely absent in any simple graph?

    • Loops and directed arcs
    • Multiple edges and cycles
    • Loops and vertices
    • Loops and multiple edges

  3. How many edges does a tree with 9 vertices have?

    • 9
    • 18
    • 8
    • 7

  4. A tree has 5 vertices. One vertex has degree 3, another has degree 2, and the remaining vertices are leaves of degree 1. How many leaves are there?

    • 3
    • 2
    • 1
    • 4

  5. If two simple graphs both have 4 vertices and 3 edges, must they be isomorphic?

    • Not necessarily
    • Always
    • Only if tree
    • Never

  6. Which graph property must be preserved under graph isomorphism?

    • Vertex labelling
    • Degree sequence
    • Layout drawing
    • Edge orientation

  7. Can two graphs with 5 vertices be isomorphic if they have 6 and 7 edges respectively?

    • Only if bipartite
    • Yes
    • No
    • Only if planar

  8. A tree has 7 vertices. If one leaf and its edge are removed, how many edges are left?

    • 6
    • 5
    • 4
    • 7

  9. A connected graph has 6 vertices and 9 edges. How many edges must be removed to leave a spanning tree?

    • 9
    • 4
    • 3
    • 5

  10. A connected graph has v vertices and v - 1 edges. Which kind of graph must it be?

    • A tree
    • A complete graph
    • A cycle
    • A graph containing a loop

  11. Which connected graph has four vertices, each of degree 2?

    • Cycle graph C4
    • Complete graph K4
    • Path graph P4
    • Star graph K1,3

  12. Which tree on five vertices has one central vertex of degree 4?

    • Complete graph K5
    • Cycle graph C5
    • Star graph K1,4
    • Path graph P5

  13. A tree has 8 vertices. Two vertices have degree 3, two vertices have degree 2, and all the other vertices are leaves. How many leaves does the tree have?

    • 5
    • 4
    • 3
    • 2

  14. Which degree sequence could belong to a tree on six vertices?

    • 2, 2, 2, 2, 2, 2
    • 4, 4, 1, 1, 1, 1
    • 3, 3, 1, 1, 1, 1
    • 2, 2, 2, 2, 2, 1

  15. Having the same degree sequence is what type of condition for graph isomorphism?

    • Necessary but insufficient
    • Sufficient only
    • Necessary and sufficient
    • Neither necessary nor sufficient

  16. How many non-isomorphic trees are there on four vertices?

    • 2
    • 1
    • 4
    • 3

  17. How many non-isomorphic trees are there on five vertices?

    • 4
    • 3
    • 2
    • 5

  18. Why are a path on 4 vertices and a cycle on 4 vertices not isomorphic?

    • Different edge counts
    • Different chromatic numbers
    • Both are disconnected
    • Different vertex counts

  19. What must a connected graph with ten vertices and ten edges contain?

    • A Hamiltonian cycle
    • At least one cycle
    • Exactly two cycles
    • No cycles at all

  20. How many spanning trees does the cycle graph C4 have?

    • 2
    • 3
    • 4
    • 1

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