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## Cycle . graph theory

### Set

 $V,E$ … set
 $\langle V,E,\psi\rangle \in \mathrm{it}(E,V)$
 $\langle V,E,\psi\rangle$ … path $|V|\ge 3$
 $u,v\in V$ $a$ … sequence in $V,\ \forall i.\ a_{i+|V|}=a_i$ $i\in\mathbb N$
 $\exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge})$

### Discussion

A path is a graph which can fully be described by a repeating sequence of vertices.