
Eulerian Graphs Quiz

Quiz
•
Mathematics
•
12th Grade
•
Hard

Patrick McPherson
Used 1+ times
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which condition must be true for a graph to be Eulerian?
All vertices with non-zero degree are connected, and exactly two vertices have odd degrees.
All vertices with non-zero degree are connected, and all vertices have even degrees.
All vertices must have the same degree.
The graph must be a complete graph.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is an Eulerian circuit?
A path that visits every vertex exactly once.
A path that visits every edge exactly once and starts and ends at the same vertex.
A path that visits every edge exactly once but can start and end at different vertices.
A path that visits some edges more than once.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a graph with 5 vertices where each vertex is connected to every other vertex, how many edges are there?
5
10
15
20
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which statement is true for Eulerian paths?
An Eulerian path exists if and only if exactly zero vertices have odd degrees.
An Eulerian path exists if and only if exactly two vertices have odd degrees.
An Eulerian path exists if and only if all vertices have even degrees.
An Eulerian path exists if and only if more than two vertices have odd degrees.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Apply Euler's theorem: If a graph has 6 vertices and each vertex has a degree of 4, how many edges does the graph have?
10
12
24
6
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following graphs is not Eulerian?
A graph where all vertices have even degrees.
A graph with three vertices of degrees 2, 4, and 6.
A complete graph with five vertices.
A graph with four vertices, each connected to every other vertex.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the minimum number of edges a simple graph with 4 vertices needs to be Eulerian?
2
3
4
6
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