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K–10Mathematics K–10 Syllabus (2022)

Record of changes
OverviewRationaleAimOutcomesContentAssessmentGlossaryTeaching and learning support

Content

Stage 5

Introduction to networks (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Examine and describe a graph/network

  • Describe a Loading  as a collection of Loading  (nodes or vertices) interconnected by Loading  (Loading ) that can represent systems in the real world

  • Examine real-world applications of networks such as social networks, supply chain networks and communication infrastructure, and explore other applications of networks

  • Explain that the terms Loading  and network are interchangeable

  • Identify and define elements of a graph including Loading , Loading  and Loading 

  • Explain that a given graph can be drawn in different ways

Define a planar graph and apply Euler’s formula for planar graphs

  • Define a Loading  as any graph that can be drawn in the plane so that no 2 edges cross

  • Define a non-planar graph as a graph that can never be drawn in the plane without some edges crossing

  • Demonstrate that some graphs that have crossing edges are still planar if they can be redrawn so that no 2 edges cross

  • Identify the number of Loading  in a planar graph

  • Describe and apply Euler’s formula for planar graphs: v-e+f=2, where v = vertices,  e = edges and f = faces

Explain the concept of Eulerian trails and circuits in the context of the Königsberg bridges problem

  • Explain that a Loading  graph is a graph that is in one piece, so that any 2 vertices are connected by a Loading 

  • Define a Loading  on a graph to be a sequence of vertices and edges of a graph

  • Explain the difference between Loading , Loading , path and Loading 

  • Relate the definition of a trail to an Eulerian trail as a walk in which every edge in the graph is included exactly once

  • Relate the definition of a circuit to an Eulerian circuit that is defined as an Eulerian trail that ends at its starting point

  • Relate Euler’s Seven Bridges of Königsberg network problem to the definition of an Eulerian trail or circuit

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