Eulerian and Hamiltonian Walks (HSC SSCE Mathematics Standard): Quizzes
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Practise the questions
10 questions from this quiz
What is the key focus of Eulerian walks compared to Hamiltonian walks?
What is the key focus of Eulerian walks compared to Hamiltonian walks?
Eulerian: edges; Hamiltonian: vertices
What defines an Eulerian circuit?
What defines an Eulerian circuit?
Every edge once, same start & end
What defines an Eulerian trail?
What defines an Eulerian trail?
Every edge once, different start & end
For an Eulerian circuit to exist, what must be true about vertex degrees?
For an Eulerian circuit to exist, what must be true about vertex degrees?
All vertices must have even degree
For an Eulerian trail to exist, how many vertices must have an odd degree?
For an Eulerian trail to exist, how many vertices must have an odd degree?
Exactly two
If a graph has four vertices with odd degree, what Eulerian walks does it contain?
If a graph has four vertices with odd degree, what Eulerian walks does it contain?
Neither trail nor circuit
What is a Hamiltonian cycle?
What is a Hamiltonian cycle?
Visits each vertex once, returns to start
How can you identify if a Hamiltonian path exists in a graph?
How can you identify if a Hamiltonian path exists in a graph?
Careful inspection, no simple rule
In a Hamiltonian path, must all edges of the graph be used?
In a Hamiltonian path, must all edges of the graph be used?
No, only all vertices must be visited
What is a traversable graph?
What is a traversable graph?
A graph containing an Eulerian trail