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Networks · Part 1 of 5
3 exam-style questions with model answers, plus 4 quick multi-choice questions — every question on this part of the standard, grouped by the 1 page of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A network has nodes P, Q, R, S and T. The arcs are , , , , , . Write down the degree of each node and verify your answer with the handshake rule.
A courier depot D serves four drop-off points W, X, Y and Z. Travel is possible D–W (12 min), D–X (9 min), W–X (5 min), W–Y (14 min), X–Y (7 min), Y–Z (6 min) and X–Z (15 min). Draw the network, and explain what the model does and does not represent about the real road system.
Prove that every network must have an even number of odd-degree nodes, and use the result to explain why a network with exactly one odd node cannot exist.