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IB Mathematics: Applications and Interpretation HL · AHL 1: Graph Theory · AHL 1.1

Graphs and their vocabulary Problem set A Answers

Skills

    1. (a) Yes
    2. (b) Yes
    3. (c) No
    1. (a) A 2, B 4, C 2, D 3, E 3, F 2
    2. (b) The degrees add up to 16 and there are 8 edges: the sum is twice the number of edges
    1. (a) 6 vertices, 6 edges
    2. (b) No. It contains a cycle
    1. (a) 6
    2. (b) 21
    1. (a) 5 vertices, 4 edges
    2. (b) No
    3. (c) No

In context

    1. (a) N: 2, P: 3, Q: 4, E: 3
    2. (b) Yes, for example P–N–Q–P–E–Q–E
    1. (a) 6 vertices, 9 edges
    2. (b) B, degree 5
    3. (c) 47 km
    1. (a) Yes
    2. (b) Yes
    3. (c) Yes

Stretch

    1. (a) 7
    2. (b) Three vertices have degree 4, so each is joined to every other vertex. Then each degree 1 vertex is joined to all three of them, so its degree is at least 3, not 1
    1. (a) \(n^2-n-90=0\)
    2. (b) n = 10

jmaths.xyz · AI HL · AHL 1.1 What is a graph? Vertices, edges and trees