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k-regular graph
Set
| $n\in\mathbb N, n\ge 1$ |
| $ Q_n\equiv\langle V,E \rangle $ |
| $ V=\{0,1\}^n $ |
| $ v,w\in V $ |
| $ k\in\mathbb N, 1\le k\ne n $ |
| $ \{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
Requirements
