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path_._graph_theory [2014/02/09 03:18] nikolaj |
path_._graph_theory [2014/03/21 11:11] |
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| - | ===== Path . graph theory ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $V,E$ ... set | | ||
| - | | @#FFBB00: $\langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ | | ||
| - | |||
| - | | @#55EE55: $\langle V,E,\psi\rangle $ ... simple graph | | ||
| - | |||
| - | | @#DDDDDD: $ u,v\in V $ | | ||
| - | | @#DDDDDD: $ a$ ... sequence in $V$ | | ||
| - | | @#DDDDDD: $ i\in\mathbb N$ | | ||
| - | |||
| - | | @#55EE55: $d(v)\neq 0$ | | ||
| - | | @#55EE55: $ \exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge}) $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | A path is a graph which can fully be described by a sequence of vertices. | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Simple graph]], [[Connected graph]] | ||
| - | === Requirements === | ||
| - | [[Sequence]], [[Vertex degree]] | ||
