Mathematics Standard • Year 11 • Networks • Lesson 3
Paths, Walks, Trails & Circuits · Apply
Trace routes through a network and decide which route constraints they satisfy.
Practice
Unless a question says otherwise, treat each network as a simple undirected graph: edges are unordered vertex pairs, with no loops or duplicate edges. Show your reasoning in the answer space; an edge list is enough.
Q1 · Park circuit. A park network has edges PQ, QR, RS, SP, PR and RT. Classify P–Q–R–P. 3 marks
Q2 · Repeated edge. For that network, classify P–R–S–P–R. 2 marks
Q3 · Reach the lookout. Using the park network, give a shortest path from Q to T and its length. 2 marks
Q1 · Park circuit
A closed trail and circuit of length 3: it uses PQ, QR and RP once each. It is also a cycle, since only the start/end vertex P repeats.
Q2 · Repeated edge
It is a walk, but not a trail: PR is used twice. It is not a path because vertices repeat.
Q3 · Reach the lookout
Q–R–T has length 2 (QR and RT). No direct Q–T edge exists, so no one-edge path is possible.