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Graphs and Trees are useful in visualizing data and the relations within and between data sets. Conversely




Question;Graphs and Trees are useful in visualizing data and the;relations within and between data sets. Conversely, it is also important to be;able to represent graphs as databases or arrays, so that programs for;processing the data can be written. Part I: Adjacency Matrix and Shortest Path;Construct a graph based on the adjacency matrix that appears below. Label all;nodes with indices consistent with the placement of numbers within the matrix.?0;6 0 5 0? | 6 0 1 0 3 | | 0 1 0 4 8 | | 5 0 4 0 0 |?0;3 8 0 0? Describe the graph and why it is consistent with the;matrix. How many simple paths are there from vertex 1 to vertex 5?;Explain.Which is the shortest of those paths? Part II: Trees Construct and;describe a tree that indicates the following: A college president has 2;employees who answer directly to him or her, namely a vice president and;provost. The vice president and provost each have an administrative assistant.;Three deans answer to the provost, and the heads of finance and alumni;relations answer to the vice president. Each dean oversees three department;chairpersons, and each department chair oversees several faculty in each of;their respective departments. Suppose that the professional correspondences are;the same as above, with the addition that there is also a direct working;relationship between the college president and the head of alumni relations (it;is not necessary to draw this). Would the graph still be a tree? Why or why;not?


Paper#61134 | Written in 18-Jul-2015

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