k-regular graph

Set

context $n\in\mathbb N, n\ge 1$
definiendum $ Q_n\equiv\langle V,E \rangle $
postulate $ V=\{0,1\}^n $
for all $ v,w\in V $
range $ k\in\mathbb N, 1\le k\ne n $
postulate $ \{v,w\}\in E \leftrightarrow \exists! k.\ \pi_k(v)\neq \pi_k(w) $

Discussion

The n-cube $Q_n$ is the graph with vertices being n-tuples which are connected exactly if they differ by one coordinate.

Examples

$V(Q_2)=\{\langle 0,0\rangle,\langle 0,1\rangle,\langle 1,0\rangle,\langle 1,1\rangle\}$

$E(Q_2)=\{\{\langle 0,0\rangle,\langle 0,1\rangle\},\{\langle 0,0\rangle,\langle 1,0\rangle\},\{\langle 0,1\rangle,\langle 1,1\rangle\},\{\langle 1,0\rangle,\langle 1,1\rangle\}\}$

… that's a square.

Parents

Subset of

Regular graph

Context

Cartesian product