Planar graphs, paths and cycles
General Mathematics · Unit 4 — Investing and netw orking · Graphs and networks
Learning objectives (8)
LO-1Apply Euler’s formula to solve problems relating to planar graphs. 𝑣 + 𝑓 − 𝑒 = 2 where 𝑣 is number of vertices, 𝑓 is number of faces and 𝑒 is number of edgesLO-2Solve practical problems involving semi-Eulerian graphs and Eulerian graphs.LO-3Solve practical problems involving semi-Hamiltonian graphs and Hamiltonian graphs (by trial-and-error methods only). General Mathematics 2025 v1.3LO-4Solve practical problems to determine the shortest path between two vertices in a weighted graph (by trial-and-error methods only).LO-5Understand the meaning of Eulerian trail, semi-Eulerian graph, Eulerian circuit and Eulerian graph, and the conditions for their existence.LO-6Understand the meaning of Hamiltonian path, semi-Hamiltonian graph, Hamiltonian cycle and Hamiltonian graph.LO-7Understand the meaning of planar graph and face.LO-8Understand the meaning of walk, trail, path, open walk, open trail, open path, closed walk, closed trail (circuit), closed path (cycle), connected graph and bridge.
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