plumiGraph theory: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.1 Graph theory, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 9 questions on Graph theory, as a list
- June 2025, AS Decision 1, Q3 (14 marks): 3 10 3 8 12 6 9 8 4 6 9 2 4 10 15 14 30 3 E G H D B A C F J Figure 2 [The total weight of the network is 153] Figure 2 models a network of roads in a town, wher
- June 2024, Decision 1, Q4 (8 marks): (a) Explain why it is not possible to draw a graph with exactly six nodes with degrees 1, 2, 3, 4, 5 and 6 (1) A tree, T, has exactly six nodes. The degrees of
- June 2023, Decision 1, Q1 (7 marks): A B D C E Figure 1 Figure 1 shows the graph G. (a) State whether G is Eulerian, semi-Eulerian, or neither, giving a reason for your answer. (1) (b) Write down a
- June 2023, AS Decision 1, Q5 (8 marks): A D B E C F 3x + 2 2x + 1 5x – 6 5x – 8 2x – 2 x + 4 x + 5 x + 7 Figure 4 [The weight of the network is 20x + 3] Figure 4 shows a graph G that contains 8 arcs a
- June 2022, AS Decision 1, Q3 (14 marks): A C B D E F 4 G H 10 12 7 15 13 3 8 11 6 4 5 10 12 Figure 2 [The total weight of the network is 120] (a) Explain what is meant by the term “path”. (2) (b) State
- November 2021, Decision 1, Q1 (4 marks): A B C D E U V W X Y Figure 1 A Hamiltonian cycle for the graph in Figure 1 begins C, V, E, X, A, W, …. (a) Complete the Hamiltonian cycle. (1) (b) Hence use the
- November 2020, Decision 1, Q6 (11 marks): C G E D B A F 19 24 65 42 21 y 15 24 34 45 x 31 Figure 4 [The total weight of the network is 320 + x + y] (a) State, with justification, whether the graph in Fi
- November 2020, AS Decision 1, Q3 (11 marks): A B C D E F G H 30 25 8 42 15 23 10 12 2x + 10 3x – 2 17 29 20 7 Figure 2 [The weight of the network is 5x + 246] (a) Explain why it is not possible to draw a g
- June 2019, AS Decision 1, Q1 (6 marks): (a) Draw the graph K5 (1) (b) (i) In the context of graph theory explain what is meant by ‘semi-Eulerian’. (ii) Draw two semi-Eulerian subgraphs of K5, each hav
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