Discrete Mathematics

The study of discrete (non-continuous) structures.

Graph Theory

• Graph — Vertices and edges
• Vertex — Node
• Edge — Connection
• Degree — Number of edges at vertex
• Path — Sequence of edges
• Cycle — Path starting and ending at same vertex
• Connected Graph — Path between any two vertices
• Tree — Connected acyclic graph
• Spanning Tree — Tree containing all vertices
• Euler Path — Traverses every edge once
• Hamilton Path — Visits every vertex once
• Bipartite Graph — Two-colorable
• Complete Graph — Every vertex connected
• Planar Graph — Can draw without crossings
• Isomorphism — Structure-preserving bijection
• Adjacency Matrix — Matrix representation
• Adjacency List — List representation

Combinatorics

• Permutation — Bijection from set to itself
• Combination — Subset of size k
• Binomial Coefficient — C(n,k)
• Binomial Theorem — (a+b)^n expansion
• Pigeonhole Principle — n items in m containers
• Inclusion-Exclusion — |A ∪ B| = |A| + |B| - |A ∩ B|
• Recurrence Relation — a_n defined from previous
• Fibonacci Sequence — F_n = F_{n-1} + F_{n-2}
• Generating Function — Formal power series