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Year 12
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General Mathematics
Graphs and networks
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Graphs and networks
1
Count the vertices, edges and loops of a graph
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2
Degrees, the degree sum, and even and odd vertices
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3
Graph types, subgraphs, connection models and method selection
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4
Connected graphs and bridges
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5
Identify isomorphic graphs
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6
Planar graphs and drawings in planar form
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7
Faces and Euler's formula
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Adjacency matrices
8
Represent a network in a matrix
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9
Identify the network a connection matrix describes
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Exploring and travelling
10
Classify a route: walk, trail, path, circuit or cycle
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11
Eulerian trails and circuits: existence and identification
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12
Hamiltonian paths and cycles
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Weighted graphs and shortest paths
13
Read a weighted graph
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14
The shortest path by inspection
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Dijkstra's algorithm
15
Dijkstra's algorithm for shortest distances and routes
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Trees and minimum connectors
16
Trees and spanning trees
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17
Minimum spanning trees by Prim's and Kruskal's algorithms
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18
A full network investigation
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Chapter 9
Chapter 11