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STANDARDS

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US-TX

Math

Texas Math

Discrete Mathematics for Problem Solving: Graph theory. The student applies the concept of graphs to determine possible solutions to real-world problems.

Explain the concept of graphs.
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Use graph models for simple problems in management science.
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Determine the valences of the vertices of a graph.
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Identify Euler circuits in a graph.
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Solve route inspection problems by Eulerizing a graph.
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Determine solutions modeled by edge traversal in a graph.
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Compare the results of solving the traveling salesman problem (TSP) using the nearest neighbor algorithm and using a greedy algorithm.
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Distinguish between real-world problems modeled by Euler circuits and those modeled by Hamiltonian circuits.
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Distinguish between algorithms that yield optimal solutions and those that give nearly optimal solutions.
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Find minimum-cost spanning trees using Kruskal's algorithm.
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Use the critical path method to determine the earliest possible completion time for a collection of tasks.
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Explain the difference between a graph and a directed graph.
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