- Mathematics General
- Year 12
Graphs and Networks
approx. 14 hrs
2 topics
41 concepts
Develop extensive understanding of Graphs and Networks and the skills for examination success.
approx. 14 hrs
2 topics
41 concepts
Develop extensive understanding of Graphs and Networks and the skills for examination success.
The Graphs and Networks program is an essential part of the Year 12 Mathematics General course as outlined in the Australian curriculum. We show students how to use graphs and networks to represent and analyse everyday situations. They conduct analysis on information contained in graphs and networks and communicate conclusions using appropriate mathematical language, notation and diagrams.
This learning program is made up of the following 2 topics, broken down into 41 concepts.
Using Euler's formula to determine element values of a connected planar graph
Identify planar graphs
Redraw a graph in planar form
Construct a graph from an adjacency matrix
Construct an adjacency matrix
Determine the degree of a vertex
Identify elements of a graph including dots, vertices, edges, loops and faces
Verify Euler's rule given a connected planar graph
Identify connected graphs and bridges
Draw directed and weighted bipartite graphs
Determine the maximum flow for any section of sequential edges of a directed graph
Use crashing to reduce the completion time of a project
Use the Hungarian algorithm to determine an optimum allocation in order to minimise cost
Identify isomorphic graphs
Determine the float time for activities in an activity network
Determine the critical path for an activity network
Determine the overall minimum completion time for a project using critical path analysis
Use forward scanning to determine the earliest starting time of activities in an activity network
Reading a graph to write down the list of vertices in order of a walk, trail, path, circuit or cycle
Use backward scanning to determine the latest starting time of activities in an activity network
Write down a precedence table or activity chart from an activity network
Create an activity network from a precedence table or activity chart
Decide when to use dummy activities in an activity network
Determine the maximum flow as equal to the minimum cut capacity
Describe the flow of material through a directed graph
Determine cut capacities
Define and describe a directed graph (digraph)
Application of eulerian trails and circuits to contextual problems
Identify eulerian trails and circuits
Determine the shortest path through a directed graph using Dijkstra's algorithm
Identify hamiltonian paths and cycles
Application of hamiltonian paths and cycles to contextual problems
Identify weighted graphs and networks
Identify traversable graphs
Identify and describe the movement around a graph as a walk, trail, path, circuit or cycle
Use Prim's algorithm to obtain a minimum spanning tree
Solving connector problems
Identify tree structures from a graph including spanning trees
Finding the shortest path through a network by inspection
Finding the shortest path through a network by Dijkstra's algorithm
Demonstrate the meaning of, and use, the terms: subgraph, simple graph, complete graph, bipartite graph, digraph, arc, weighted graph and network
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