SOL Prep

Graph Theory

Virginia SOL DM.GT.1

Represent problems using vertex-edge graphs and analyze graph properties.

Study DM.GT.1 with SOL PrepBack to Discrete Mathematics

What students need to be able to do

  • 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.