Georgia standard · Mathematics

`AFM.AQR.7`Graph Theory Applications

Apply graph theory to solve contextual, mathematical problems and to explain real-life phenomena.

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Expectations

Use, apply, and prove graph properties.
- AFM.AQR.7.1
  Identify simple graphs, complete graphs, complete bipartite graphs, and trees. Identify graphs that have Euler and Hamiltonian cycles.
- AFM.AQR.7.2
  Construct the complement and the line graph of a graph.
- AFM.AQR.7.3
  Use the adjacency matrix of a graph to determine the number of walks of length n in a graph.
- AFM.AQR.7.4
  Prove statements about graph properties.
Apply graph theory in context.
- AFM.AQR.7.5
  Prove that every connected graph has a minimal spanning tree.
- AFM.AQR.7.6
  Use Kruskal’s algorithm and Prim’s algorithm to determine the minimal spanning tree of a weighted graph.

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