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n-cube [2014/02/10 22:57] nikolaj old revision restored (2014/02/08 21:49) |
n-cube [2014/03/21 11:11] |
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| - | ===== k-regular graph ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $n\in\mathbb N, n\ge 1$ | | ||
| - | | @#FFBB00: $ Q_n\equiv\langle V,E \rangle $ | | ||
| - | |||
| - | | @#55EE55: $ V=\{0,1\}^n $ | | ||
| - | |||
| - | | @#FFFDDD: $ v,w\in V $ | | ||
| - | | @#DDDDDD: $ k\in\mathbb N, 1\le k\ne n $ | | ||
| - | |||
| - | | @#55EE55: $ \{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]] | ||
| - | === Requirements === | ||
| - | [[Cart]] | ||
