Stack Exchange
How to draw the arcs in the following figure

\documentclass[a4paper, 12pt, oneside]{article}
    \usepackage{pst-all}
    \usepackage{tikz}
    \begin{document}

\tikzset{every path/.style=thick,
       acteur/.style={
         circle,
         fill=black,
        thick,
         inner sep=1pt,
         minimum size=.13cm
       },
       curvy line/.style={decorate,,rounded corners=2pt,decoration={random steps,segment length=3mm,
       amplitude=1mm}}}
\tikzset{curvy line/.style={decorate,decoration={snake,segment length=8.5mm,
   amplitude=1mm}}}

\begin{figure}[hbt!]
\begin{center}    
\begin{tikzpicture}[scale=.7,every label/.append style={font=\scriptsize}]
\begin{scope}   

      \node (a1) at (0,0) [acteur,label=below:{$x$}]{};   

      \node (a2) at (1.5,0) [acteur,label=below:{$x'$}]{};
      \node (a3) at (1.5,1.5) [acteur,label=left:{}]{};
      \node (a9) at (0,1.5) [acteur,label=left:{}]{};
      \node (a7) at (.75,3) [acteur,label=right:{}]{};

      \draw  (a1) -- (a2);
      \draw [dashed] (a2) -- (a3);

      \draw  [dashed](a3) -- (a7);

      \draw [dashed] (a1) -- (a9);
      \draw [dashed] (a9) -- (a7);
      % \draw (3,1.5) circle (.8);
      % \draw (.75, 4.6) circle (.8);
      % \draw (-1.5, 1.5) circle (.8);
      \draw (1.5,1.5) -- (2.7,1.5);
      \draw [dashed] (1.5,1.5) -- (2.7,1.1);
      \draw [dashed] (1.5,1.5) -- (2.7,1.8);
      \draw [dashed] (.75,3) -- (.99,4.2);
      \draw [dashed] (.75,3) -- (.50,4.2);
      \draw [dashed] (0,1.5) -- (-1.12,1.8);
      \draw [dashed] (0,1.5) -- (-1.12,1.2);
      % \draw [dotted](1.85,.5) to[bend left=100] (1.85,2.5);
      % \draw (2.5,2.5) arc (0:315:1.75cm and 1cm);
      % \draw[dashed] (1.5,1.5)[bend left=90] arc (0:180:1.5cm);

      \draw (.75,3) -- (.75,4.2);
      \draw (0,1.5)-- (-1.1,1.5);
      \node at (.75,-1) {$U_1$}; 
      \node at (-1.6,1.5) {\scriptsize{$T_1$}}; 
      \node at (0.75,4.8) {\scriptsize{$T_2$}}; 
      \node at (3.3,1.5) {\scriptsize{$T_3$}}; 

\end{scope}
\end{tikzpicture} 

\caption{The solid edge in $U_1$ denotes the matching edge. The graph $U_1$ lies in $\mathcal{U}_1$ while $U_2$ lies in 
$\mathcal{U}_2$. }
\end{center}
\end{figure}

\end{document}

How to draw the arc curves in the figure. Give an idea.

Please consider accepting answers to earlier questions you got. Otherwise users may hesitate to answer this. You keep using e.g. the answer that provided you with curvy lines, why don't you just accept it?

Something like this?

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{positioning}

\begin{document}
    \begin{tikzpicture}[
node distance = 12mm and 12mm,
     acteur/.style = {circle, draw, fill=black,
                      minimum size=1.5mm, node contents={}
                      },
every label/.style = {font=\footnotesize},
 every path/.style = thick,
        bend angle = 15
                        ]
% nodes
\node (a1)  [acteur,label=below:$x$];
\node (a2)  [acteur, above=of a1];
\node (a3)  [acteur, above right=of a2];
\node (a4)  [acteur, below right=of a3];
\node (a5)  [acteur, below=of a4,label=below:{$x'$}];
% lines
\draw [dashed]  (a1) -- (a2) -- (a3) -- (a4) -- (a5);
\draw           (a1) -- node[below=5mm] {$U_1$} (a5);
% lines at T_1
\draw (a2) -- ++ (-1,0) node[left] {$T_1$};
\draw[dashed] (a2) to[bend  left] ++ (-1,-0.5)
              (a2) to[bend right] ++ (-1, 0.5);     
% lines at T_2
\draw (a3) -- ++ (0,1) node[above] {$T_2$};
\draw[dashed] (a3) to[bend  left] ++ (-0.5,1)
              (a3) to[bend right] ++ ( 0.5,1);
% lines at T_3
\draw (a4) -- ++ (1,0) node[right] {$T_3$};
\draw[dashed] (a4) to[bend  left] ++ (1, 0.5)
              (a4) to[bend right] ++ (1,-0.5);
    \end{tikzpicture}
\end{document}

