Discrete mathematics and combinatorics
Model graphs, trees, and combinatorial structures and give complete counts with structural reasons.
Meaning
Discrete mathematics and combinatorics study arrangements, selections, and connections of distinguishable objects. Graph vertices and edges abstract problems involving routes, networks, and schedules.
Example
If stations A, B, and C are connected only by routes A–B and B–C, travel from A to C must pass through B. This connected graph with no cycle is an example of a tree. Lines crossing in a drawing do not automatically create a station or vertex. The actual connections must be specified separately.
Practice for this concept
Scope and references
Topics
Graphs, trees, combinatorial structures, relationships between discrete objects
Learning goal
Model graphs, trees, and combinatorial structures and give complete counts with structural reasons.
Helpful background
Explore the counting, sets, logic, and basic proofs needed for the chosen topic.
Graph structure and constrained counting
These tasks do not assess general graph algorithms or classification of all combinatorial structures.