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NSW Curriculum
NSW Education Standards Authority

K–10Mathematics K–10 Syllabus

Record of changes
Implementation for K–2 from 2023 and 3–10 from 2024
Expand for detailed implementation advice

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 network as a collection of objects (nodes or vertices) interconnected by lines (edges) 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 graph and network are interchangeable

  • Identify and define elements of a graph including vertex, edge and degree

  • 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 planar graph 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 faces in a planar graph

Explain the concept of Eulerian trails and circuits in the context of the Königsberg bridges problem
  • Explain that a connected graph is a graph that is in one piece, so that any 2 vertices are connected by a path

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

  • Explain the difference between trail, circuit, path and cycle

  • 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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