\begin{tikzpicture}[scale=\scalepuncturedpentagon,font=\small] 
\node (a) at (0,0) [fill,circle,inner sep=2pt] {};
\draw (0,0) circle (1.25cm);
\foreach \x in {-144,-72,0,72,144} {
   \begin{scope}[rotate=\x]
    \node (\x) at (0,-1.25) [fill,circle,inner sep=1pt] {};
   \end{scope}
}
%\draw (a) node [above] {$0$};
\draw (0) node [below] {$\mathbf 4$}; % v1
\draw (72) node [right] {$\mathbf {1}$}; %v2
\draw (144) node [above right]  {$\mathbf 2$}; %v3
\draw (-144) node [above left] {$\mathbf 3$}; %v4
\draw (-72) node [left] {$\mathbf 2$}; % v5
\draw[] (a) to (-144); 
\draw[] (a) to (-72);
\draw[] (a) to (0);
\draw[out=5,in=30] (0) to  (-144);
\draw[out=0,in=-80] (0) to  (144);
\end{tikzpicture}