Walks, Trails, Paths, Circuits, and Cycles (VCE SSCE General Mathematics): Flashcards

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Walks, Trails, Paths, Circuits, and Cycles
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Walk definition

Sequence of edges linking vertices; can repeat edges & vertices

Trail definition

Walk with no repeated edges (vertices can repeat)

Path definition

Walk with no repeated edges and no repeated vertices

Circuit definition

Walk starting & ending at same vertex; no repeated edges

Cycle definition

Closed walk; no repeated edges or vertices (except start/end)

Repetition allowed in walks

Both edges and vertices

Repetition allowed in trails

Vertices only (not edges)

Repetition allowed in paths

None (no repeated edges or vertices)

Closed walk meaning

Walk that starts and ends at the same vertex

Circuit vs cycle difference

Circuit allows repeated vertices; cycle doesn't (except start/end)

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