Hypercube graph
The 4-dimensional hypercube.
The \(4\)-dimensional hypercube, \(Q_4.\)

A hypercube graph is a graph that depicts a hypercube, which is kinda like a higher-dimensional version of a cube. The symbol \(Q_n\) denotes the graph of an \(n\)-dimensional hypercube.

\(Q_n\) is always an \(n\)-regular graph with \(2^n\) vertices and \(2^{n-1}n\) edges.

Each vertex can be assigned an \(n\)-bit binary string such that if the binary strings of any two vertices differ by just \(1\) bit, they are adjacent. So, \(Q_n\) can be drawn by writing out every possible \(n\)-bit binary string and connecting the ones that are \(1\) bit off from each other.

To draw \(Q_n\) more easily, you can just draw \(2\) copies of \(Q_{n-1}\) and then connect the corresponding vertices. Kind of like how if you draw \(2\) squares \((Q_2)\) and then connect each of their corresponding vertices with an edge, you get a cube \((Q_3).\) This same pattern can be extended to draw \(Q_4\), which is called a "tesseract."

Logic & Proofs
Integer • Rational number • Inequality • Real number • Theorem • Proof • Statement • Proof by exhaustion • Universal generalization • Counterexample • Existence proof • Existential instantiation • Axiom • Logic • Truth • Proposition • Compound proposition • Logical operation • Logical equivalence • Tautology • Contradiction • Logic law • Predicate • Domain • Quantifier • Argument • Rule of inference • Logical proof • Direct proof • Proof by contrapositive • Irrational number • Proof by contradiction • Proof by cases • Summation • Disjunctive normal form
Set Theory
Set • Element • Empty set • Universal set • Subset • Power set • Cartesian product • String • Binary string • Empty string • Set operation • Set identity • Set proof
Functions
Function • Floor function • Ceiling function • Inverse function
Algorithms
Algorithm • Pseudocode • Command • Asymptotic notation • Time complexity • Atomic operation • Brute-force algorithm
Relations
Relation • Reflexive relation • Symmetric relation • Transitive relation • Relation composition • Equivalence relation • Equivalence class
Number Theory
Integer division • Linear combination • Division algorithm • Modular arithmetic • Prime factorization • Greatest common divisor • Least common multiple • Primality test • Factoring algorithm • Euclid's theorem • Prime number theorem • Euclidean algorithm
Induction
Proof by induction • Fibonacci sequence • Proof by strong induction • Well-ordering principle • Sequence • Factorial • Recursive definition
Combinatorics
Rule of product • Rule of sum • Bijection rule • Permutation • Combination • Complement rule • Experiment • Outcome • Sample space • Event • Probability • Probability distribution • Uniform distribution • Multiset • Sixfold way • Inclusion-exclusion principle • Pigeonhole principle
Graph Theory
Graph • Walk • Subgraph • Regular graph • Complete graph • Empty graph • Cycle graph • Hypercube graph • Bipartite graph • Component • Eulerian circuit • Eulerian trail • Hamiltonian cycle • Hamiltonian path • Tree • Huffman tree • Substring • Forest • Path graph • Star • Spanning tree • Weighted graph • Minimum spanning tree • Greedy algorithm • Prim's algorithm
Recursion
Recursion • Recursive algorithm • Correctness proof • Divide-and-conquer algorithm • Sorting algorithm • Merge sort