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Consider the following graph:

- Complete this table by finding the degree of each vertex, and identify whether it is even or odd:

- What is the order of the graph?
- Construct the 10 x 10 adjacency matrix for the graph.
- The graph below illustrates a switching network. The weights represent the delay times, in nanoseconds, travelled by a data packet between destinations, represented by the vertices.
- Complete the following table by finding the shortest distance and the path for that distance from vertex A to the other vertices:
- What is the shortest distance between A and J and the path for that distance?
- The following graph represents a portion of the subway system of a city. The vertices on the graph correspond to subway stations, and the edges correspond to the rails. Your job is to write a program for a cleaning car to efficiently clean this portion of the subway system.
- Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once.
- Using Fleury’s algorithm, provide an optimal path to clean all the rails by passing through them only once.
- Is it possible to find an optimal path described in question 3-b that starts on any station? Explain your answer.
- Is it possible to find an optimal path described in question 3-b that starts and ends at the same station? Explain why or why not.

- Find a Hamiltonian path in the graph.
- Find a Hamiltonian circuit that will allow the engineer to inspect all of the servers. How much will the cost be for his trips?
- Is there another Hamiltonian circuit that will allow the engineer to inspect all of the servers other than your answer in question 4-b? If so, calculate the cost.
- What is the height of the tree?
- What is the height of vertex H?
- Write the preorder traversal representation of the tree.
- Write the array representation of the tree by completing the following table: