Eulerian & semi-Eulerian Graphs (Edexcel A-Level Further Mathematics): Quizzes
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Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What is an Eulerian path?
What is an Eulerian path?
A path visiting every edge exactly once
What is an Eulerian circuit?
What is an Eulerian circuit?
Visits every edge once, same start & end
What is the order (degree) of a node?
What is the order (degree) of a node?
Number of edges connected to it
For a graph to be Eulerian, what must be true about vertex orders?
For a graph to be Eulerian, what must be true about vertex orders?
All vertices have even order
How many vertices with odd order does a semi-Eulerian graph have?
How many vertices with odd order does a semi-Eulerian graph have?
Exactly two
A connected graph has vertices with orders . What type is it?
A connected graph has vertices with orders . What type is it?
Semi-Eulerian
A graph has 4 vertices with odd order. What type is it?
A graph has 4 vertices with odd order. What type is it?
Neither
How much does a loop (edge to itself) add to a vertex's order?
How much does a loop (edge to itself) add to a vertex's order?
2
In a semi-Eulerian graph, where does the Eulerian path start and end?
In a semi-Eulerian graph, where does the Eulerian path start and end?
At the two vertices with odd order
Can a disconnected graph be Eulerian?
Can a disconnected graph be Eulerian?
No, must be connected