Exploring and Travelling (VCE SSCE General Mathematics): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What is a walk in graph theory?
What is a walk in graph theory?
Sequence of edges connecting vertices
What defines a trail in a graph?
What defines a trail in a graph?
A walk where no edge is repeated
Which type of movement through a graph is the most restrictive?
Which type of movement through a graph is the most restrictive?
Path
What is a circuit in graph theory?
What is a circuit in graph theory?
A trail starting and ending at same vertex
What distinguishes a cycle from other graph movements?
What distinguishes a cycle from other graph movements?
Path starting and ending at same vertex
How does a circuit differ from a cycle?
How does a circuit differ from a cycle?
Circuit can repeat vertices; cycle cannot
When does an Eulerian trail exist in a connected graph?
When does an Eulerian trail exist in a connected graph?
Exactly zero or two odd-degree vertices
What condition guarantees an Eulerian circuit exists?
What condition guarantees an Eulerian circuit exists?
All vertices have even degree
What does a Hamiltonian path do?
What does a Hamiltonian path do?
Visits every vertex exactly once
What is the key difference between Eulerian and Hamiltonian?
What is the key difference between Eulerian and Hamiltonian?
Eulerian covers edges; Hamiltonian vertices