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

Graphs and their vocabulary Problem set B Answers

Skills

    1. (a) No
    2. (b) Yes
    3. (c) No
    1. (a) P 2, Q 5, R 2, S 3, T 3, U 3
    2. (b) The degrees add up to 18 and there are 9 edges: the sum is twice the number of edges
    1. (a) 7 vertices, 6 edges
    2. (b) No. It is not connected and it contains a cycle
    1. (a) 8
    2. (b) 36
    1. (a) 5 vertices, 5 edges
    2. (b) Yes
    3. (c) No

In context

    1. (a) S: 3, K: 3, I: 3, J: 3
    2. (b) No: four vertices have odd degree
    1. (a) 6 vertices, 8 edges
    2. (b) Q, degree 4
    3. (c) 95 minutes
    1. (a) Yes
    2. (b) No
    3. (c) No

Stretch

    1. (a) 9
    2. (b) Three vertices have degree 5, 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) \(n^2-n-132=0\)
    2. (b) n = 12

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