General Mathematics · Unit 4 · Graphs and networks · Planar graphs, paths and cycles
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A regional council has received complaints that rubbish bins along five streets are not being emptied regularly. The table shows which streets are directly connected by intersections. Determine whether the waste truck can complete a route that travels along each street exactly once without retracing any street, starting and finishing at the depot located at intersection P.
A waste collection service needs to plan a route that traverses every street in a suburb exactly once, returning to the depot. The street network has 8 vertices (intersections), 12 edges (streets), and all vertices have even degree except for two vertices which have odd degree. Which statement correctly describes the route planning problem?
A park ranger must inspect all walking trails in a nature reserve. The network below shows the trails connecting six rest points (A, B, C, D, E, F). Each edge represents a trail. Determine whether it is possible for the ranger to start at one rest point, walk each trail exactly once, and finish at a different rest point. Justify your response.