Traversing a Graph (AQA A-Level Further Maths): Flashcards

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Traversing a Graph
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Walk definition

Journey w/ no restrictions on repeating edges or vertices

Trail definition

Walk where no edge is repeated

Path definition

Walk w/ no edges or vertices repeated

Cycle definition

Closed path, starts/ends at same vertex, no repeats

Hamiltonian cycle definition

Cycle visiting every vertex exactly once

Tree definition

Connected graph with no cycles

Eulerian graph condition

All vertices have even degree

Semi-Eulerian graph condition

Exactly two vertices with odd degree

Non-Eulerian graph condition

More than two vertices with odd degree

No. of odd degree vertices in any graph

Must be even

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