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General Mathematics · Unit 4 · Graphs and networks · Planar graphs, paths and cycles

Understand the meaning of Eulerian trail, semi-Eulerian graph, Eulerian circuit and Eulerian graph, and the conditions for their existence.

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Question 1

A tourist information centre has created a map showing walking paths connecting six viewing platforms (F, G, H, J, K, L) around a coastal reserve. The table below shows which platforms are directly connected by walking paths. (a) Determine whether the network is Eulerian, semi-Eulerian, or neither. Justify your answer using the degree of each vertex. (2 marks) (b) The centre wants to create a guided tour that uses every path exactly once. Determine whether this is possible, and if so, identify a suitable starting platform. Justify your response. (2 marks)

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