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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.