# Definition of closed walks on a graph. How to enumerate the vertices?

In my definition, this is a closed walk? If yes, how can I enumerate the vertices? In this picture, who is $$v_1, v_2,...$$?

Definition: A closed walk in a graph is defined to be ordered collection of vertices $$(v_1,v_2,...,v_n)$$ such that $$v_i$$ and $$v_{i+1}$$ are neighbours for all $$1 \leq i \leq n-1$$, and $$v_n$$ and $$v_1$$ are neighbours. Note that the walk is allowed to visit the same vertex or traverse the same edge on more than one occasion.

• No, the picture is not a closed walk, because a closed walk is a sequence of vertices, and the picture is not a sequence of vertices. – Misha Lavrov Dec 13 '18 at 21:45
• @MishaLavrov could you give me an example of closed walk that we have at least two visits the same vertex and/or at least two traverse the same edge? I can't imagine an example. Thanks – Pedro Salgado Dec 13 '18 at 21:49
• Get a "triangle" graph with vertices $v_1,\, v_2,\, v_3$. $(v_1,\, v_2,\, v_3, \,v_1,\, v_2,\, v_3)$ is one of such closed walks. – Lucas Henrique Dec 13 '18 at 22:00