Path

#Definition

Let $v_{0}$ and $v_{n}$ be vertices in a graph $G$ . A path in $G$ from $v_{0}$ to $v_{n}$ of length $n$ is an alternating sequence of $n + 1$ vertices and $n$ edges, $v_{0} e_{1} v_{1} e_{2} \dots v_{n - 1} e_{n} v_{n}$ , in which edge $e_{i}$ is incident on vertices $v_{i - 1}$ and $v_{i}$ for every $i = 1, \dots, n$

Note that in a simple graph, to denote a path we just need to list the sequence of vertices since two vertices are connected by only one edge, e.g. $v_{0} v_{1} \dots v_{n}$