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IB Mathematics: Applications and Interpretation HL · AHL 1: Graph Theory · AHL 1.3

Walks, trails, paths, circuits and cycles Problem set B Answers

Skills

  1. P–Q–S–R; P–U–S–R (2 paths)

  2. Q–R–U–T–Q; Q–S–T–U–Q; Q–T–U–R–Q; Q–U–T–S–Q (4 cycles)

    1. (a) Walk
    2. (b) Cycle
    3. (c) Trail
    4. (d) Circuit
    1. (a) T and U
    2. (b) For example T–S–P–T–R–Q–T–U

In context

    1. (a) P–Q–R–S; P–Q–T–S; P–U–T–S
    2. (b) P–Q–T–U–P; P–U–T–Q–P
    1. (a) Degrees: P 2, Q 4, R 2, S 2, T 2, U 2
    2. (b) For example P–Q–R–U–T–Q–S–P
    3. (c) No: it is a circuit, and Q is visited more than once
    1. (a) Route 1 and Route 2
    2. (b) Route 2

Stretch

    1. (a) 12
    2. (b) 20
    1. (a) P–Q–R–P–T–S–R–T–U
    2. (b) P–Q–R–P–T–S–R–T–U–P

jmaths.xyz · AI HL · AHL 1.3 Walks, trails, paths, circuits and cycles