Unit 1 Worksheet - LS Home Page

Name ______________________________
Unit 1 Worksheet
I. Consider the following graph:
A
Date ______________________
E
F
B
D
C
1. Is the graph connected?
2. How many vertices are on the graph?
3. How many edges are on the graph?
4. What is the valence of vertex A?
5. What is the valence of vertex F?
6. Does the graph have an Euler Circuit?
7. What is the best description for A, B,C,D,E,F ? A. path B. circuit C. Euler circuit
8. What is the best description for A, B,C,D,E,A ? A. path B. circuit C. Euler circuit
9. What is the best description for A, B,F,E,C,F,B,C,D,E,A ?
A. path B. circuit C. Euler circuit
II.
10. If a graph is connected and ___________, the graph will have an Euler Circuit.
a. the graph has an even number of vertices
b. the graph has an even number of edges
c. the graph has all vertices of even valence
d. the graph has only two odd vertices

11. If a graph has 14 odd vertices, what is the minimum number of edges required to Eulerize
the graph?
12. What is the minimum number of edges required to Eulerize the graph? Sketch the
Eulerization.
13. What is the minimum number of edges required to Eulerize the graph? Sketch the
Eulerization.
14. What is the minimum number of edges required to Eulerize the graph? Sketch the
Eulerization.
15. Which of the following is a real world application of Eulerizing a graph?
a. After a storm, a health department worker inspects all the houses of a small village to check
for damage.
b. After a snow storm, a town plow plows all the streets of the town.
c. A state agency sends an agent to all the schools in MA.