Discrete Mathematics · Graph Theory
Virginia SOL DM.GT.1
Virginia SOL DM.GT.1 is part of the Graph Theory strand in Discrete Mathematics (Math). Under this Standards of Learning objective, students represent problems using vertex-edge graphs and analyze graph properties. Below is what DM.GT.1 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice DM.GT.1 for the Virginia SOL test.
What SOL DM.GT.1 means
Represent problems using vertex-edge graphs and analyze graph properties.
Skills you’ll practice for DM.GT.1
- Illustrate basic terminology of graph theory (vertex, edge, graph, degree of a vertex).
- Use graphs to map situations where vertices represent objects and edges represent relationships.
- Identify and describe degree and connectedness in graphs.
- Determine whether a graph is planar or nonplanar.
- Analyze the relationship between faces, edges, and vertices using Euler's formula (F = E - V + 2).
- Use directed graphs (digraphs) to represent situations with traversal restrictions.
- Determine when graphs are trees.
Key concepts covered by DM.GT.1
- graph theory
- vertex
- edge
- degree of a vertex
- graph mapping
- vertices
- edges
- relationship representation
- connectedness
- graph properties
- planar graphs
- nonplanar graphs
- Euler's formula
- faces
- directed graphs
- digraphs
- traversal restrictions
- trees
- acyclic graphs
How to study and practice SOL DM.GT.1
Start with a quick diagnostic to see whether DM.GT.1 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.2 — Solve problems using circuits, cycles, Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits.
- 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.1
What is Virginia SOL DM.GT.1?
SOL DM.GT.1 is a Discrete Mathematics Standard of Learning in the Graph Theory strand. It expects students to represent problems using vertex-edge graphs and analyze graph properties.
What skills does SOL DM.GT.1 cover?
SOL DM.GT.1 is assessed on 7 skills: illustrate basic terminology of graph theory (vertex, edge, graph, degree of a vertex); use graphs to map situations where vertices represent objects and edges represent relationships; identify and describe degree and connectedness in graphs; determine whether a graph is planar or nonplanar; analyze the relationship between faces, edges, and vertices using Euler's formula (F = E - V + 2); use directed graphs (digraphs) to represent situations with traversal restrictions; determine when graphs are trees.
What strand of Discrete Mathematics is SOL DM.GT.1 in?
SOL DM.GT.1 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.1?
Start with a diagnostic to see whether DM.GT.1 is already solid, then work the 7 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.