- Mathematics General
- Year 12
Graphs and Networks
approx. 11 hrs
11 topics
22 concepts
Develop a thorough understanding of Graphs and Networks to confidently solve a range of related problems.
approx. 11 hrs
11 topics
22 concepts
Develop a thorough understanding of Graphs and Networks to confidently solve a range of related problems.
In this area of study students explore graphs and networks and their use to model practical situations. Students will learn to identify different types of graphs and their features, including the application of Euler's formula. We will help students navigate a given network to determine the type of movement of each graph and solve a range of related problems.
This learning program is made up of the following 11 topics, broken down into 22 concepts.
Identify elements of a graph including dots, vertices, edges, loops and faces
Determine the degree of a vertex
Demonstrate the meaning of, and use, the terms: subgraph, simple graph, complete graph, bipartite graph, digraph, arc, weighted graph and network
Identify isomorphic graphs
Identify connected graphs and bridges
Redraw a graph in planar form
Identify planar graphs
Using Euler's formula to determine element values of a connected planar graph
Verify Euler's rule given a connected planar graph
Construct an adjacency matrix
Construct a graph from an adjacency matrix
Reading a graph to write down the list of vertices in order of a walk, trail, path, circuit or cycle
Identify traversable graphs
Identify and describe the movement around a graph as a walk, trail, path, circuit or cycle
Investigate the Konigsberg bridge problem
Identify eulerian trails and circuits
Application of eulerian trails and circuits to contextual problems
Identify hamiltonian paths and cycles
Application of hamiltonian paths and cycles to contextual problems
Identify weighted graphs and networks
Finding the shortest path through a network by inspection
Finding the shortest path through a network by Dijkstra's algorithm
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