Complete the following in a paper of 1–2 pages:
Vertex 
Degree 
Even/Odd 
A 


B 


C 


D 


E 


F 


G 


H 


b. Complete the following table by finding the shortest distance and the path for that distance from vertex A to the other vertices:
Vertex 
Shortest Distance from A 
Path from A 
B 


C 


D 


E 


F 


G 


H 


I 


b. Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once.
c. Using Fleury’s algorithm, provide an optimal path to clean all the rails by passing through them only once.
d. Is it possible to find an optimal path described in question 3b that starts on any station? Explain your answer.
e. Is it possible to find an optimal path described in question 3b that starts and ends at the same station? Explain why or why not.
A network engineer lives in City A, and his job is to inspect his company’s servers in various cities. The graph below shows the cost (in U.S. dollars) of travelling between each city that he has to visit.
. Find a Hamiltonian path in the graph.
a. Find a Hamiltonian circuit that will allow the engineer to inspect all of the servers. How much will the cost be for his trips?
b. Is there another Hamiltonian circuit that will allow the engineer to inspect all of the servers other than your answer in question 4b? If so, calculate the cost.
Consider the following binary tree:
. What is the height of the tree?
a. What is the height of vertex H?
b. Write the preorder traversal representation of the tree.
c. Write the array representation of the tree by completing the following table:
Vertex 
Left Child 
Right Child 
A 


B 


C 


D 


E 


G 


H 


I 


J 


K 


L 


M 


N 


O 


P 


Q 


R 


S 


T 


Consider the following weighted graph:
Last Name Begins With 
a 
b 
A–K 
10, 14, 16, 5 
4, 6, 9, 11 
L–Q 
5, 11, 13, 8 
2, 7, 12, 15 
R–Z 
3, 8, 10, 19 
13, 15, 17, 18 
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