In the lecture in uni, the lecture said
A path in digraph G is a walk in which no vertex appears more than once.
I could understand this. But he gives a example in graphs,(not digraphs)
said
A path of length 3 in the graph could be the sequence
{c,d},{d,e},{e,a}
But I understood that in a path, there's no vertex appears more than once so there's no edge that go both side. I thought that if they are going both sides then the vertices appears twice.
But all of {c,d},{d,e},{e,a} are going both sides. I mean (c,d) and (d,c) are also in the set of edges.
So I'm wondering why did he say those are a path of length 3.
$\textbf{Definition:}$ Let $x,y$ be (not necessarily distinct) vertices in an undirected graph $G=(V, E)$. An $x-y$ walk in $G$ is a finite alternating squence $$x=x_0, e_1, x_1, e_2, x_2, e_3, \cdots, e_{n-1}, e_n, x_n=y$$ of vertices and edges from G, starting at vertex $x$ and ending at vertex $y$ and involving the n edges $e_i=\{x_{i-1}, x_i\}$, where $1\leq i\leq n$.
Then $\textit{length}$ of this walk $n$, the number of edges in the walk.
$\textbf{Definition:}$ If no vertex of the $x-y$ walk occurs more han once, then the walk is called $x-y$ $\textit{path}$.
$\{c,d\},\{d,e\},\{e,a\}$ means $c-a$ walk. $c-a$ walk means $c-a (=cdea)$ path. Because, no vertex of the $c-a$ walk occurs more than once.
In given graph $\{c, d\}=\{d,c\}$. Actually, it is true for all undirected graph. So, $\{c, d\}=\{d,c\}$ used once to do $c-a$ walk .