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Running Head: DISCRETE STRUCTURES1MAT-FP 2051: Discrete MathematicsAssessment 5: Discrete StructuresCapella UniversitySeptember 15, 2020Janaya Hoskins
DISCRETE STRUCTURES2Part 1: Using Graphs and Matrices to Represent SystemsAssume you have been recently hired by the Department of Transportation (DoT) to analyzemotorized vehicle traffic flows. Your initial goal is to analyze the traffic and traffic delays in alarge metropolitan area.You choose to use a weighted graph to represent this scenario. Remember that a graph is acollection of nodes (or vertices) and edges. Each edge will have a corresponding weight.1.Describe how you would construct such a weighted graph. What do the nodesrepresent? What do the edges represent? What values would the weights represent? Is thisgraph a tree? Justify your design. Feel free to include an example in your description.Toanalyze the traffic on the metropolitan area we can construct a weighted graph whichn represents important small cities in the metropolitan area. Edges represent roads connecting thecities, and weight corresponds to the traffic on a particular time, which more specifically isthe number vehicles per minute on that road. This weighted graph cannot be a tree, since therecan be cycles, as we have multiple roads connecting two cities.For example,In the above graph A,B,C,D,E,F,G,H and I represents different small cities in the metropolitanarea , the edges shows different roads connecting the cities and the weight on the edges showsthe flow capacity or the maximum number of vehicles that can be on the road for a particularinstant of time. Obviously, this is not a tree since it includes many cycles.

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Term
Spring
Professor
N/A
Tags
Graph Theory, Shortest path problem, Flow network

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