Eulerian Trails and Circuits (Extension) (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 an Eulerian trail?
What is an Eulerian trail?
A path using each edge exactly once
What is an Eulerian circuit?
What is an Eulerian circuit?
An Eulerian trail starting & ending same
How many odd-degree vertices allow an Eulerian trail?
How many odd-degree vertices allow an Eulerian trail?
Zero or two
What condition on vertex degrees allows an Eulerian circuit?
What condition on vertex degrees allows an Eulerian circuit?
All vertices have even degree
If a graph has zero odd vertices, what exists?
If a graph has zero odd vertices, what exists?
Both trail and circuit
With two odd vertices, where must an Eulerian trail start and end?
With two odd vertices, where must an Eulerian trail start and end?
Start at one odd vertex, end at other
What if a graph has more than two odd vertices?
What if a graph has more than two odd vertices?
Neither trail nor circuit exists
What is the degree of a vertex?
What is the degree of a vertex?
Number of edges connected to it
How do Eulerian trails and circuits relate?
How do Eulerian trails and circuits relate?
Every circuit is a trail
Why are Eulerian concepts useful in mail delivery?
Why are Eulerian concepts useful in mail delivery?
Minimizing time and distance traveled