plumiGraph theory: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on DA.1 Graph theory, 2019–2025, 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 22 questions on Graph theory, as a list
- June 2025, Paper 3 Discrete, Q8 (10 marks): The connected planar graph G has n2 vertices, 2n edges and 3n – 4 faces, where n is an integer. 8 (a) (i) Show that n = 2 [3 marks] 8 (a) (ii) Hence, write down
- June 2025, AS Paper 2 Discrete, Q2 (1 mark): A simple-connected graph has n vertices, where n ≥ 2 State the minimum number of edges of the graph. Circle your answer. [1 mark] n – 1 n n + 1 n(n – 1) 2
- June 2025, AS Paper 2 Discrete, Q3 (3 marks): A graph is shown below. A C B D 3 (a) Complete the table, to show the degree of each vertex. [1 mark] Vertex Degree A B C D 3 (b) A student makes two statements
- June 2024, Paper 3 Discrete, Q3 (1 mark): The simple-connected graph G has the adjacency matrix A B C D A 0 1 1 1 B 1 0 1 0 C 1 1 0 1 D 1 0 1 0 Which one of the following statements about G is true? Tic
- June 2024, AS Paper 2 Discrete, Q1 (1 mark): A connected planar graph has v vertices, e edges and f faces. Which one of the formulae below is correct? Circle your answer. [1 mark] v + e + f = 2 v – e + f =
- June 2024, AS Paper 2 Discrete, Q2 (1 mark): Find an expression for the number of edges in the complete bipartite graph, Km,n Circle your answer. [1 mark] m n m – n m + n mn
- June 2024, AS Paper 2 Discrete, Q3 (1 mark): Which one of the graphs shown below is semi-Eulerian? Tick (✓) one box. [1 mark]
- June 2023, Paper 3 Discrete, Q1 (1 mark): The simple-connected graph G is shown below. The graph G has n faces. State the value of n Circle your answer. [1 mark] 2 3 4 5
- June 2023, Paper 3 Discrete, Q8 (9 marks): The graph G is shown below. 8 (a) (i) State, with a reason, whether or not G is simple. [2 marks] 8 (a) (ii) A student states that G is Eulerian. Explain why th
- June 2023, AS Paper 2 Discrete, Q1 (1 mark): The graph G has 8 vertices and 13 edges as shown in the diagram below. P Q S V T R U W Graph H is a simple-connected subgraph of graph G Which of the following
- June 2023, AS Paper 2 Discrete, Q8 (7 marks): (a) The graph G has 2 vertices. The sum of the degrees of all the vertices of G is 6 Draw G [1 mark] 8 (b) The planar graph P is Eulerian, with at least one ver
- June 2022, Paper 3 Discrete, Q1 (1 mark): The graph G has a subgraph isomorphic to K5, the complete graph with 5 vertices. Which of the following statements about G must be true? Tick (3) one box. [1 ma
- June 2022, Paper 3 Discrete, Q2 (1 mark): Graph A is a connected planar graph with 12 vertices, 18 edges and n faces. Find the value of n Circle your answer. [1 mark] 4 8 28 32 for the next question
- June 2022, AS Paper 2 Discrete, Q1 (2 marks): The connected graph G is shown below. The graphs A and B are subgraphs of G Both A and B have four vertices. 1 (a) The graph A is a tree with x edges. State the
- June 2022, AS Paper 2 Discrete, Q5 (3 marks): (a) A connected planar graph has 9 vertices, 20 edges and f faces. Use Euler’s formula for connected planar graphs to find f [2 marks] 5 (b) The graph J, shown
- November 2021, Paper 3 Discrete, Q6 (8 marks): (a) A connected planar graph has (x + 1)2 vertices, (25 + 2x × 2y) edges and ( y × 1)2 faces, where x > 0 and y > 0 Find the possible values for the number of v
- November 2021, AS Paper 2 Discrete, Q5 (7 marks): An adjacency matrix for the simple graph G is shown below. A B C D E A 0 1 1 0 0 B 1 0 1 0 0 C 1 1 0 0 0 D 0 0 0 0 1 E 0 0 0 1 0 5 (a) Using the adjacency matri
- November 2020, Paper 3 Discrete, Q5 (4 marks): The planar graph P is shown below. 5 (a) Determine the number of faces of P. [2 marks] 5 (b) Akwasi claims that P is semi-Eulerian as it is connected and it has
- November 2020, AS Paper 2 Discrete, Q2 (1 mark): The graph G has 5 vertices and 6 edges, as shown below. Which of the following statements describes the properties of G? Tick (3) one box. [1 mark] G is Euleria
- November 2020, AS Paper 2 Discrete, Q4 (4 marks): The connected planar graph P is Eulerian and has at least one vertex of degree x. Some of the properties of P are shown in the table below. Number of vertices N
- June 2019, Paper 3 Discrete, Q2 (1 mark): The graph D is shown in the diagram below. Which of the graphs below is a subdivision of D? Circle your answer. [1 mark]
- June 2019, Paper 3 Discrete, Q4 (6 marks): The connected planar graph P has the adjacency matrix A B C D E A 0 1 1 0 1 B 1 0 1 0 1 C 1 1 0 1 1 D 0 0 1 0 1 E 1 1 1 1 0 4 (a) Draw P [1 mark] 4 (b) Using Eu
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