Path . graph theory

Set

context $V,E$ … set
definiendum $\langle V,E,\psi\rangle \in \mathrm{it}(E,V) $
postulate $\langle V,E,\psi\rangle $ … simple graph
range $ u,v\in V $
range $ a$ … sequence in $V$
range $ i\in\mathbb N$
postulate $d(v)\neq 0$ 
postulate $ \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.

Theorems

The only paths which are non-bipartite are cycles of odd order.

Parents

Subset of

Simple graph, Connected graph

Context

Sequence, Vertex degree