Discrete Mathematics · Graph Theory
Virginia SOL DM.GT.2
Virginia SOL DM.GT.2 is part of the Graph Theory strand in Discrete Mathematics (Math). Under this Standards of Learning objective, students solve problems using circuits, cycles, Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. Below is what DM.GT.2 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice DM.GT.2 for the Virginia SOL test.
What SOL DM.GT.2 means
Solve problems using circuits, cycles, Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits.
Skills you’ll practice for DM.GT.2
- Determine whether a graph has an Euler circuit or path and identify it if it exists.
- Determine whether a graph has a Hamilton circuit or path and identify it if it exists.
- Count the number of Hamilton circuits for a complete graph with n vertices.
- Use an Euler circuit algorithm to solve optimization problems.
Key concepts covered by DM.GT.2
- Euler circuit
- Euler path
- graph traversal
- Hamilton circuit
- Hamilton path
- Hamilton circuits
- complete graphs
- combinatorics
- Euler circuit algorithm
- optimization problems
- graph algorithms
How to study and practice SOL DM.GT.2
Start with a quick diagnostic to see whether DM.GT.2 is already solid, then work each skill above with guided notes, flashcards, and SOL-style practice questions. For official released items, see our Virginia SOL practice tests guide and how to study for the SOL test.
Related Discrete Mathematics standards in Graph Theory
- DM.GT.1 — Represent problems using vertex-edge graphs and analyze graph properties.
- DM.GT.3 — Apply graphs to conflict-resolution problems such as graph coloring, scheduling, matching, and optimization.
- DM.GT.4 — Recognize and apply algorithms to solve configuration, conflict-resolution, and sorting problems.
- DM.GT.5 — Use algorithms to schedule tasks and determine minimum project time.
Frequently asked questions about SOL DM.GT.2
What is Virginia SOL DM.GT.2?
SOL DM.GT.2 is a Discrete Mathematics Standard of Learning in the Graph Theory strand. It expects students to solve problems using circuits, cycles, Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits.
What skills does SOL DM.GT.2 cover?
SOL DM.GT.2 is assessed on 4 skills: determine whether a graph has an Euler circuit or path and identify it if it exists; determine whether a graph has a Hamilton circuit or path and identify it if it exists; count the number of Hamilton circuits for a complete graph with n vertices; use an Euler circuit algorithm to solve optimization problems.
What strand of Discrete Mathematics is SOL DM.GT.2 in?
SOL DM.GT.2 belongs to the Graph Theory reporting strand of the Discrete Mathematics Virginia Standards of Learning.
How do I study and practice for SOL DM.GT.2?
Start with a diagnostic to see whether DM.GT.2 is already solid, then work the 4 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.