General Mathematics · Unit 4 · Graphs and networks · Planar graphs, paths and cycles
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The diagram shows a network of five walking tracks connecting four viewing platforms (F, G, H, J) at a nature reserve. Determine the degree of each vertex, then identify whether this network is Eulerian, semi-Eulerian, or neither. Justify your response.
A town council is planning a maintenance route for their street sweeper. The network below shows the streets connecting five intersections: \(A\) (Airport Road), \(F\) (Fire Station), \(H\) (Hospital), \(L\) (Library), and \(M\) (Market Square). Which statement correctly describes this network?
A council is planning walking routes through a botanical garden. The network diagram shows the pathways connecting various garden features. Which statement about the network is correct?
A park has four shelters (A, B, C, D) connected by walking paths as shown in the diagram. Identify whether the graph is Eulerian or semi-Eulerian. Justify your response.
The diagram represents six walkways connecting four picnic shelters (F, G, H, and J) in a park. Identify whether the network is Eulerian or semi-Eulerian. Justify your response.
A network of walking paths connects several monuments in a heritage site. The graph below shows the monuments as vertices and the paths as edges. Which of the following correctly classifies this graph?
Identify whether the graph shown is Eulerian, semi-Eulerian, or neither. Justify your response.
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)