Walks, Trails, Paths, Circuits, and Cycles (VCE SSCE General Mathematics): Flashcards
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Walk definition
Walk definition
Sequence of edges linking vertices; can repeat edges & vertices
Trail definition
Trail definition
Walk with no repeated edges (vertices can repeat)
Path definition
Path definition
Walk with no repeated edges and no repeated vertices
Circuit definition
Circuit definition
Walk starting & ending at same vertex; no repeated edges
Cycle definition
Cycle definition
Closed walk; no repeated edges or vertices (except start/end)
Repetition allowed in walks
Repetition allowed in walks
Both edges and vertices
Repetition allowed in trails
Repetition allowed in trails
Vertices only (not edges)
Repetition allowed in paths
Repetition allowed in paths
None (no repeated edges or vertices)
Closed walk meaning
Closed walk meaning
Walk that starts and ends at the same vertex
Circuit vs cycle difference
Circuit vs cycle difference
Circuit allows repeated vertices; cycle doesn't (except start/end)
