Euler Circuit
Hamiltonian Circuits
Vertices
Random Math Facts
Random Facts
100
How can you determine if a graph is an Euler Path? How can you determine if a graph is an Euler Circuit?
Path:If there are only 2 ODD DEGREE VERTICES.
Circuit: ALL EVEN DEGREE VERTICES
100
What do Hamiltonian Graphs use each of ONE TIME ONLY?
Hint: Edges or vertices?
A vertex is used ONLY ONCE for Hamiltonian.
100
What is a vertex?
A point that connects edges together in a graph.
100
What is 2+2?
5
100
What is Mr. Nations' middle name?
Douglus
200
Is the following map an Euler Circuit or Path?
Draw in the correct circuit or path.
Euler Path
200
True or false:
ALL Hamiltonian circuits are also Hamiltonian paths.
True. All circuits are also considered paths.
200
How many edges can connect to a vertex?
Infinity :)
200
What is the meaning of life?
42
200
What city is Mr. Nations from?
Lawrence, KS
300
Is the following map an Euler Circuit or Path?
Draw in the correct circuit or path.
Euler Path
300
Is the following map a Hamiltonian Circuit or Path? Draw in the Circuit or Path.
Hamiltonian Circuit
300
What is the DEGREE of a vertex?
The number of edges connected to the vertex.
300
What is a math teachers favorite type of tree?
A Geometry!
300
What year was Diet Coke created?
1982
400
Is the graph below an Euler Path, Circuit, or Neither?
Draw in the correct circuit or path.
Euler Circuit
400
Use the "Nearest Neighbor" Algorithm to determine the total time and route through each vertex. Start at Vertex A.
AEBCDA = 30
400
What is the degree of Vertex A?
3
400
What are 10 things you can always count on?
Your fingers.
400
What is the only continent that does not have glaciers?
Australia
500
Find the shortest time through the entire map. Add all of the total times and give the route.
Total time: 45
500
FINAL JEOPARDY (MUST BE DONE LAST):
Use the SORTED EDGES ALGORITHM to find the quickest Hamiltonian Circuit for the graph.
The edges used, in order, are:
AE, CE, AB, CD, BD
500
What is the degree of vertex E?
3
500
Why can't a nose be 12 inches?
Because it would then be a foot!
500
What is the only even prime number?
2