
Hamiltonian Circuits and Complete Graphs

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard

Sophia Harris
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a complete graph?
A graph with a single edge.
A graph where each vertex is connected to every other vertex.
A graph with no edges.
A graph with only one vertex.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a complete graph with five vertices, how many routes visit each city once?
24
48
12
60
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the factorial notation for the number of routes in a complete graph with four choices?
3!
5!
6!
4!
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do Hamiltonian circuits differ from routes in a complete graph?
They include all possible routes.
They do not return to the starting point.
They return to the starting point and have no duplicates.
They return to the starting point and have duplicates in reverse order.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many unique Hamiltonian circuits are there in a complete graph with five vertices?
24
12
60
48
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the formula for calculating the number of routes in a complete graph with n vertices?
n factorial
(n-1) factorial
n squared
n cubed
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In a complete graph with seven vertices, how many possible routes are there?
120
360
720
840
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