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Hypercube graph
Set
| $ n\in\mathbb N, n\ge 1 $ |
| $ V\equiv \{0,1\}^n $ |
| $Q_n\equiv \langle V,E\rangle$ |
| $ k\in\mathbb N,1\le k\le n $ |
| $ v,w\in V $ |
| $ \{v,w\}\in E\leftrightarrow \exists!k.\ \pi_k(v)\neq\pi_k(w) $ |
Discussion
The Hypercube graph, also called n-cube, has vertices all n-tuples of 0's and 1's and two such vertices are connected iff they differ in one coordinate.
E.g. $V(Q_2)=\{\langle 0,0\rangle,\langle 0,1\rangle,\langle 1,0\rangle,\langle 1,1\rangle\}$ and there are all but the diagonal relations are edges in the graph. Clearly $Q_n$ is just a square.
Parents
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Requirements
