VCE Together Year 12 Walks, Trails, Paths, Cycles and Circuits
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# Walks, Trails, Paths, Cycles and Circuits

Walks, Trails, Paths, Cycles and Circuits is a part of the VCE Further Maths topic Networks and Decision Mathematics. It is a part of the subtopic Exploring and Travelling problems. The following definitions are important:

• Walk: a sequence of edges and vertices in a network.
• Trail: a walk where no edges are repeated.
• Path: a trail that connects all vertices.
• Cycle: a trail that finishes on the vertex it begins on. No vertex is repeated.
• Circuit: a path that begins and ends on the same vertex. Vertices can be repeated.

### Network Travel Terminology

The following video introduces the terminology involved in network travel including; walks, trails, paths, circuits.

### Identifying the walk

The following video explains how to identify which type of walk a network undertakes using the appropriate. terminology

### Traversable and Non-Traversable Graphs

traversable graph has a trail that includes every edge. A non-traversable graph has a trail that does not include every edge. The following video explains the difference between traversable and non-traversable graphs.

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