\begin{figure}[htp]\label{fig:derived-graph}
    \centering
    \begin{tikzpicture}
   [scale=0.65,line width=1.2]
    \coordinate (1) at (0, 3);
    \coordinate (2) at (3/1.71, 0);
    \coordinate (3) at (-3/1.71, 0);
    
    \coordinate (4) at (0, 3 + 0.4);
    \draw (1) arc(270:360+270:0.4);
    %\path [draw = black, postaction = {on each segment = {mid arrow = red}}]
    %(0, 3+0.8) arc(90:120:0.4);
    
    
    \path [draw = red, postaction = {on each segment = {mid arrow = red}}]
    (1)--(2);
     \path [draw = blue, postaction = {on each segment = {mid arrow = red}}]
     (3)--(1);
     \path [draw = green, postaction = {on each segment = {mid arrow = red}}]
    (2) to [bend left] (3);
    
     \path [draw = purple, postaction = {on each segment = {mid arrow = red}}]
    (3) to [bend left] (2);
    
    \draw[fill] (1) circle [radius=0.1];
    \node at (0.5, 3) {$1$};
    \draw[fill] (2) circle [radius=0.1];
    \node at (3/1.71 + 0.5, 0) {2};
    \draw[fill] (3) circle [radius=0.1];
    \node at (-3/1.71-0.5, 0) {3};
    
    
    \node at (1 + 0.4, 3+ 0.5) {$(a, 321)$};
    \node at (3/1.71/2 + 1.1, 3/2) {$(b, 231)$};
    \node at (-3/1.71/2 - 1.2, 3/2) {$(d, 123)$};
    \node at (0, 0.85 + 0.1) {$(e, 132)$};
    \node at (0, -0.85 - 0.1) {$(c, 123)$};
    \end{tikzpicture}
    \caption{A permutation-voltage graph $\Gamma$.}
    \label{fig:perm-voltage-graph}
\end{figure}