at (e) {{$v_3$}};
\node[anchor = west ]  at (h) {{$v_0$}};

\end{tikzpicture}$$

Another gradient vector field on the Möbius band is

$$\begin{tikzpicture}[
    decoration={markings,mark=at position 0.6 with {\arrow{triangle 60}}},
    ]


\filldraw[fill=black!30, draw=black] (0,0)--(6,0)--(6,2)--(0,2)--cycle;

\node[inner sep=1pt, circle, fill=black] (a) at (0,0) [draw] {};
\node[inner sep=1pt, circle, fill=black] (b) at (2,0) [draw] {};
\node[inner sep=1pt, circle, fill=black] (c) at (4,0) [draw] {};
\node[inner sep=1pt, circle, fill=black] (d) at (6,0) [draw] {};
\node[inner sep=1pt, circle, fill=black] (e) at (0,2) [draw] {};
\node[inner sep=1pt, circle, fill=black] (f) at (2,2) [draw] {};
\node[inner sep=1pt, circle, fill=black] (g) at (4,2) [draw] {};
\node[inner sep=1pt, circle, fill=black] (h) at (6,2) [draw] {};



\draw[->-]  (b)--(a) node[midway] {};
\draw[-]  (a)--(e) node[midway] {};
\draw[-]  (a)--(f) node[midway] {};
\draw[->-]  (c)--(b) node[midway] {};
\draw[-]  (b)--(g) node[midway] {};
\draw[-]  (b)--(f) node[midway] {};
\draw[-]  (c)--(d) node[midway] {};
\draw[-]  (c)--(h) node[midway] {};
\draw[-]  (c)--(g) node[midway] {};
\draw[-]  (h)--(d) node[midway] {};
\draw[->-]  (e)--(f) node[midway] {};
\draw[-]  (f)--(g) node[midway] {};
\draw[->-]  (g)--(h) node[midway] {};


\draw[-triangle 60]  (1,1)--(.5,1.5);
\draw[-triangle 60]  (3,1)--(2.5,1.5);
\draw[-triangle 60]  (3.5,0)--(3.5,1);
\draw[-triangle 60]  (5,1)--(5.5,.5);



\node[anchor = north ]  at (a) {};
\node[anchor = north ]  at (b) {};
\node[anchor = north ]  at (c) {};
\node[anchor = north ]  at (d) {};
\node[anchor = south ]  at 