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finite_undirected_graph [2014/02/10 23:10] nikolaj removed |
finite_undirected_graph [2014/03/21 11:11] (current) |
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| - | ===== Hypercube graph ===== | + | ===== Finite undirected graph ===== |
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $ n\in\mathbb N, n\ge 1 $ | | + | | @#55CCEE: context | @#55CCEE: $V,E$ ... set | |
| - | | @#DDDDDD: $ V\equiv \{0,1\}^n $ | | + | |
| - | | @#FFBB00: $Q_n\equiv \langle V,E\rangle$ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ | |
| - | | @#DDDDDD: $ k\in\mathbb N,1\le k\le n $ | | + | | @#55EE55: postulate | @#55EE55: $\langle V,E,\psi\rangle $ ... undirected graph | |
| - | | @#FFFDDD: $ v,w\in V $ | | + | | @#55EE55: postulate | @#55EE55: $ E,V $ ... finite | |
| - | + | ||
| - | | @#55EE55: $ \{v,w\}\in E\leftrightarrow \exists!k.\ \pi_k(v)\neq\pi_k(w) $ | | + | |
| ==== Discussion ==== | ==== 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 ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Undirected graph]] | [[Undirected graph]] | ||
| - | === Requirements === | ||
| - | [[Cartesian product]] | ||
