---
title: "AFM.AQR.7: Graph Theory Applications (Georgia Mathematics standard)"
code: AFM.AQR.7
cite_as: Georgia Standards of Excellence, Mathematics, AFM.AQR.7
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/AFM.AQR.7
md_url: https://georgiahomeroom.org/standards/code/AFM.AQR.7.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/AFM.AQR.7.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# AFM.AQR.7: Graph Theory Applications

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

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## 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.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.