• 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.

Available in
NT QLD SA TAS VIC WA

### Overview

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.

### Topics & Concepts We Cover

This learning program is made up of the following 2 topics, broken down into 41 concepts.

• #### Graph theory 9 concepts

1. Using Euler's formula to determine element values of a connected planar graph

2. Redraw a graph in planar form

3. Identify planar graphs

5. Construct a graph from an adjacency matrix

6. Identify elements of a graph including dots, vertices, edges, loops and faces

7. Determine the degree of a vertex

8. Verify Euler's rule given a connected planar graph

9. Identify connected graphs and bridges

• #### Application of Graph Theory 32 concepts

1. Draw directed and weighted bipartite graphs

2. Use the Hungarian algorithm to determine an optimum allocation in order to minimise cost

3. Identify isomorphic graphs

4. Use crashing to reduce the completion time of a project

5. Determine the critical path for an activity network

6. Determine the overall minimum completion time for a project using critical path analysis

7. Reading a graph to write down the list of vertices in order of a walk, trail, path, circuit or cycle

8. Determine the float time for activities in an activity network

9. Use backward scanning to determine the latest starting time of activities in an activity network

10. Use forward scanning to determine the earliest starting time of activities in an activity network

11. Decide when to use dummy activities in an activity network

12. Create an activity network from a precedence table or activity chart

13. Write down a precedence table or activity chart from an activity network

14. Determine the maximum flow as equal to the minimum cut capacity

15. Determine cut capacities

16. Determine the maximum flow for any section of sequential edges of a directed graph

17. Describe the flow of material through a directed graph

18. Identify eulerian trails and circuits

19. Application of eulerian trails and circuits to contextual problems

20. Determine the shortest path through a directed graph using Dijkstra's algorithm

21. Define and describe a directed graph (digraph)

22. Identify hamiltonian paths and cycles

23. Application of hamiltonian paths and cycles to contextual problems

24. Identify weighted graphs and networks

25. Identify traversable graphs

26. Identify and describe the movement around a graph as a walk, trail, path, circuit or cycle

27. Use Prim's algorithm to obtain a minimum spanning tree

28. Solving connector problems

29. Identify tree structures from a graph including spanning trees

30. Finding the shortest path through a network by inspection

31. Finding the shortest path through a network by Dijkstra's algorithm

32. Demonstrate the meaning of, and use, the terms: subgraph, simple graph, complete graph, bipartite graph, digraph, arc, weighted graph and network

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Graphs and Networks

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

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