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Math
Virginia Math
Discrete Mathematics: Graph Theory
Illustrate the basic terminology of graph theory (e.g., vertex, edge, graph, degree of a vertex).
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Use graphs to map situations in which the vertices represent objects, and edges represent a particular relationship between objects.
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Identify and describe degree and connectedness.
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Determine whether a graph is planar or nonplanar.
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Analyze the relationship between faces, edges, and vertices using Euler’s formula (𝐹 = 𝐸 – 𝑉 + 2).
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Use directed graphs (digraphs) to represent situations with restrictions in traversal possibilities.
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Determine when graphs are trees.
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Determine whether a graph has an Euler circuit or path, and determine the circuit or path, if it exists.
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Determine whether a graph has a Hamilton circuit or path, and determine the circuit or path, if it exists.
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Count the number of Hamilton circuits for a complete graph with 𝑛 vertices.
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Use an Euler circuit algorithm to solve optimization problems.
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Model projects consisting of several subtasks, using a graph.
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Use graphs to resolve conflicts that arise in scheduling.
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Use graph coloring to determine the chromatic number of a graph.
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Recognize algorithms such as nearest neighbor, brute force, and cheapest link as they apply to graphs.
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Use Kruskal’s algorithm to determine the shortest spanning tree of a connected graph.
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Use Prim’s algorithm to determine the shortest spanning tree of a connected graph.
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Use Dijkstra’s algorithm to determine the shortest spanning tree of a connected graph.
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Specify in a digraph the order in which tests are to be performed.
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Identify the critical path to determine the earliest completion time (minimum project time).
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Use the list-processing algorithm to determine an optimal schedule.
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Create and test scheduling algorithms.
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