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Complete the following in a paper of 1–2 pages:Consider the following graph:  Complete this table by finding the degree of each vertex, and identify whether it is even or odd: VertexDegreeEven/OddA  B  C  D  E  F  G  H  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: VertexShortest Distance from APath from AB  C  D  E  F  G  H  I  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. 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.  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. Consider the following binary tree:  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:  VertexLeft ChildRight ChildA  B  C  D  E  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  Please submit your assignment.For assistance with your assignment, please use your text, Web resources, and all course materials.Grading Rubric Project CriteriaExceeds: 90%–100%Very Good: 80%–89%Meets: 70%–79%Needs Improvement: Below 70%Content
(75%)Response covers all topics indicated in the assignment and adds additional content. Response covers most topics indicated in the assignment. Response covers many of the topics indicated in the assignment.Response covers none to some of the topics indicated in the assignment. Effective Communication
(10%)Demonstrates outstanding or exemplary application of written, visual, or oral skills. Demonstrates outstanding expression of topic, main idea, and purpose. Audience is addressed appropriately. Language clearly and effectively communicates ideas and content relevant to the assignment. Errors in grammar, spelling, and sentence structure are minimal. Organization is clear. Format is consistently appropriate to assignment. Presentation and delivery are confident and persuasive (where applicable). The writing was of collegiate level with no errors in spelling or grammar.Demonstrates very good written, visual, or oral skills. Demonstrates sound expression of topic, main idea, and purpose. Audience is usually addressed appropriately. Language does not interfere with the communication of ideas and content relevant to the assignment. Errors in grammar, spelling, and sentence structure are present, but do not distract from the message. Organization is apparent and mostly clear. Format is appropriate to assignment, but not entirely consistent. The writing was of collegiate level with two or less errors in spelling or grammar.Demonstrates acceptable written, visual, or oral skills. Demonstrates reasonable expression of topic, main idea, and purpose. Sometimes, audience is addressed appropriately. Language does not interfere with the communication of ideas and content relevant to the assignment. Errors in grammar, spelling, and sentence structure are present and may distract from the message. Organization is a bit unclear. Format is inconsistent. The writing was of collegiate level with several errors in spelling or grammar.Demonstrates inadequate or partially proficient application of written, visual, or oral skills. Demonstrates inadequate or partial expression of topic, main idea, and purpose. Audience is often not addressed appropriately. Language often impedes the communication of ideas and content relevant to the assignment. Errors in grammar, spelling, and sentence structure are frequent and often distract from meaning or presentation. Organization is inadequate, confusing, and distracting. The format is inadequate and obscures meaning. The writing was less than collegiate level with numerous errors in spelling or grammar.Supporting Analysis
(15%)Analysis exceeds minimum requirements. Sources are used to support analysis, are appropriate, and are properly referenced.Basic analysis provided to support assertions. Sources are cited, appropriate, and properly referenced.Limited analysis provided to support assertions. Some sources are cited, appropriate, and properly referenced.No or inaccurate analysis, no sources are cited when needed, analysis and/or sources are not appropriate. When sources are used, they are not properly referenced.