Discrete Math

Study of mathematical structures that are fundamentally discrete rather than continuous.

Set TheoryLogic and ProofFunctions and Relations
Graph TheoryCombinatoricsNumber Theory
Cryptography and SecurityNetwork AnalysisScheduling and Planning
Breaking Down ProblemsUsing Visuals and Diagrams
Set TheoryLogic and ProofFunctions and Relati...Graph TheoryCombinatoricsNumber TheoryCryptography and Sec...Network AnalysisScheduling and Plann...Breaking Down Proble...Using Visuals and Di...
Advanced Topics

Graph Theory

What Is Graph Theory?

Graph theory studies structures made of nodes (also called vertices) connected by edges. These structures can represent networks, relationships, and connections.

Types of Graphs

  • Simple Graphs: No loops or multiple edges between the same pair of nodes.
  • Directed Graphs (Digraphs): Edges have directions (like one-way streets).
  • Weighted Graphs: Edges have values or weights.

Applications

Graphs are used to model social networks, transportation systems, and the internet.

Key Concepts

  • Path: A sequence of edges connecting nodes.
  • Cycle: A path that starts and ends at the same node.
  • Connected Graph: There's a path between every pair of nodes.

Why Study Graphs?

Graph theory helps us solve problems like finding the shortest route, detecting cycles, and understanding complex systems.

Examples

  • A subway map is a graph with stations as nodes and tracks as edges.

  • Friend connections on social media form a network graph.

In a Nutshell

Graph theory explores connections and relationships using nodes and edges, modeling real-world networks.

Key Terms

Vertex
A point or node in a graph.
Edge
A connection between two vertices in a graph.
Cycle
A path that starts and ends at the same node.
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Combinatorics