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Name ______________________________<br />
<strong>Unit</strong> 1 <strong>Worksheet</strong><br />
I. Consider the following graph:<br />
A<br />
Date ______________________<br />
E<br />
F<br />
B<br />
D<br />
C<br />
1. Is the graph connected?<br />
2. How many vertices are on the graph?<br />
3. How many edges are on the graph?<br />
4. What is the valence of vertex A?<br />
5. What is the valence of vertex F?<br />
6. Does the graph have an Euler Circuit?<br />
7. What is the best description for A, B,C,D,E,F ? A. path B. circuit C. Euler circuit<br />
8. What is the best description for A, B,C,D,E,A ? A. path B. circuit C. Euler circuit<br />
9. What is the best description for A, B,F,E,C,F,B,C,D,E,A ?<br />
A. path B. circuit C. Euler circuit<br />
II.<br />
10. If a graph is connected and ___________, the graph will have an Euler Circuit.<br />
a. the graph has an even number of vertices<br />
b. the graph has an even number of edges<br />
c. the graph has all vertices of even valence<br />
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<br />
the graph?<br />
12. What is the minimum number of edges required to Eulerize the graph? Sketch the<br />
Eulerization.<br />
13. What is the minimum number of edges required to Eulerize the graph? Sketch the<br />
Eulerization.<br />
14. What is the minimum number of edges required to Eulerize the graph? Sketch the<br />
Eulerization.<br />
15. Which of the following is a real world application of Eulerizing a graph?<br />
a. After a storm, a health department worker inspects all the houses of a small village to check<br />
for damage.<br />
b. After a snow storm, a town plow plows all the streets of the town.<br />
c. A state agency sends an agent to all the schools in MA.