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Ryan, Engineer

Category: Math Homework

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Experience: B.S. in Civil Engineering

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1. Consider the following graph: a. Complete this table

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1. Consider the following graph: a. Complete this table by finding the degree of each vertex, and identify whether it is even or odd: Vertex Degree Even/Odd A B C D E F G H b. What is the order of the graph? c. Construct the 10 x 10 adjacency matrix for the graph. 2. 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. a. 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. What are the shortest distance between A and J and the path for that distance? 3. 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. a. Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once. b. Using Fleury’s algorithm, provide an optimal path to clean all the rails by passing through them only once. c. Is it possible to find an optimal path described in question 3-b that starts on any station? Explain your answer. d. 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. 4. 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. a. Find a Hamiltonian path in the graph. b. Find a Hamiltonian circuit that will allow the engineer to inspect all of the servers. How much will the cost be for his trips? c. 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. 5. Consider the following binary tree: a. What is the height of the tree? b. What is the height of vertex H? c. Write the preorder traversal representation of the tree. d. 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

Hi, Welcome! Thank you for using the site, and thank you for requesting me. Can you post these in a Word document, or even a PDF document? It seems like there are a lot of graphics missing from these problems. Thanks, Ryan

Hi, Thanks! That looks better. I've only scanned through it, so it's possible that I may come across something else that needs clarification. If so, I'll let you know. Is there a specific deadline for completion? Ryan

Hi, I have a couple of questions about the problems in this set. In part c of #1, it asks for a "10 x 10 adjacency matrix". However, the graph for that problem only has 8 nodes. Unless your course is doing something unusual with the multiple edges between node C and node D, I don't see how we can get a 10 x 10 matrix from this graph. It seems that the adjacency matrix should only be 8 x 8. In problem #4, there is no cost shown on the graph for the edge between node D and node E, nor for the edge between node E and node C. It is not clear whether this means that the cost for those links is 0, or if this is an oversight. Can you please attempt to clarify both of these issues? Thanks, Ryan

Hey Ryan, thank you for noticing these issues. I will ask my Professor on Friday, May 08 during our weekly Live Chat Session which will be held at 7 PM CST (8 PM EST). I do not understand why the Live Chat Session is being held so late in the week, when the assignment is due on Sunday night 12 AM CST (1 AM EST).

Hi, I hope you're feeling ok today. I was wondering if you were able to get any clarification concerning those two problems during the live chat for your course. I have the rest of the solutions completed and am just waiting to hear from you about those two problems. Thanks, Ryan

Hi again, Thank you. :) I thought that I would need more time to finish this up, but it turns out that #4 can be answered satisfactorily by simply ignoring the unlabeled edges in the graph. Here are the solutions: Solutions Please feel free to ask if you have questions about any of these solutions. Thanks, Ryan