How to insert special symbol in a picture - latex

Question

I had tried this code and I want the braces in the figure as there are in the attached picture.
\begin{figure}[hbt!]
\begin{center}
\begin{tikzpicture}[
thick,
acteur/.style={
circle,
fill=black,
thick,
inner sep=2pt,
minimum size=0.2cm
}
]
\node (a1) at (-0.3,0.65) [acteur,label=below :\scriptsize{}]{};
\node (a2) at (1,0)[acteur,label=below:\scriptsize{\hspace{0.3cm}$x_{0}$}]{};
\node (a3) at (2,0) [acteur,label=below:\scriptsize{$x_{1}$}]{};
\node (a4) at (3,0) [acteur,label=below:\scriptsize{$x_{2}$}]{};
\node (a5) at (4,0) [acteur,label=above :\scriptsize{}]{};
\node (a6) at (5,0) [acteur,label=below right :\scriptsize{\hspace{-0.9cm}$x_{k-s-t}$}]{};
\node (a7) at (6.5,0) [acteur,label=below:\scriptsize{}]{};
\node (a8) at (-0.3,-0.65) [acteur,label=above:\scriptsize{}]{};
\node (a9) at (0.4,1.3) [acteur,label=above:\scriptsize{}]{};
\node (a10) at (0.4,-1.3) [acteur,label=below:\scriptsize{}]{};
\node (a11) at (6,1) [acteur,label=below:\scriptsize{}]{};
\node (a12) at (6,-1) [acteur,label=below:\scriptsize{}]{};
\node (a13) at (5.3,1.3) [acteur,label=below:\scriptsize{}]{};
\node (a14) at (5.3,-1.3) [acteur,label=below:\scriptsize{}]{};
\draw (a1) -- (a2);
\draw (a2) -- (a9);
\draw (a2) -- (a8);
\draw (a2) -- (a10);
\draw (a2) -- (a3);
\draw (a3) -- (a4);
\draw [dashed] (a4) -- (a5);
\draw (a5) -- (a6);
\draw (a6) -- (a7);
\draw (a6) -- (a11);
\draw (a6) -- (a13);
\draw (a6) -- (a12);
\draw (a6) -- (a14);
\end{tikzpicture}
\end{center}
\caption{\small{The graph $\mathcal{P}(k,s,t)$}}
\end{figure}

Answer 1

You can use the decorations library
\documentclass[12pt]{article}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\begin{figure}[hbt!]
\begin{center}
\begin{tikzpicture}[
thick,
acteur/.style={
circle,
fill=black,
thick,
inner sep=2pt,
minimum size=0.2cm
}
]
\node (a1) at (-0.3,0.65) [acteur,label=below :\scriptsize{}]{};
\node (a2) at (1,0)[acteur,label=below:\scriptsize{\hspace{0.3cm}$x_{0}$}]{};
\node (a3) at (2,0) [acteur,label=below:\scriptsize{$x_{1}$}]{};
\node (a4) at (3,0) [acteur,label=below:\scriptsize{$x_{2}$}]{};
\node (a5) at (4,0) [acteur,label=above :\scriptsize{}]{};
\node (a6) at (5,0) [acteur,label=below right :\scriptsize{\hspace{-0.9cm}$x_{k-s-t}$}]{};
\node (a7) at (6.5,0) [acteur,label=below:\scriptsize{}]{};
\node (a8) at (-0.3,-0.65) [acteur,label=above:\scriptsize{}]{};
\node (a9) at (0.4,1.3) [acteur,label=above:\scriptsize{}]{};
\node (a10) at (0.4,-1.3) [acteur,label=below:\scriptsize{}]{};
\node (a11) at (6,1) [acteur,label=below:\scriptsize{}]{};
\node (a12) at (6,-1) [acteur,label=below:\scriptsize{}]{};
\node (a13) at (5.3,1.3) [acteur,label=below:\scriptsize{}]{};
\node (a14) at (5.3,-1.3) [acteur,label=below:\scriptsize{}]{};
\draw (a1) -- (a2);
\draw (a2) -- (a9);
\draw (a2) -- (a8);
\draw (a2) -- (a10);
\draw (a2) -- (a3);
\draw (a3) -- (a4);
\draw [dashed] (a4) -- (a5);
\draw (a5) -- (a6);
\draw (a6) -- (a7);
\draw (a6) -- (a11);
\draw (a6) -- (a13);
\draw (a6) -- (a12);
\draw (a6) -- (a14);
\draw[decorate,decoration={brace,amplitude=10pt}]
(-0.5, -1) -- (-0.5, 1) node[left, midway, xshift = -10pt]{$s$ vertices};
\draw[decorate,decoration={brace,amplitude=10pt}]
(6.5, 1) -- (6.5, -1) node[right, midway, xshift = 10pt]{$t$ vertices};
\end{tikzpicture}
\end{center}
\caption{\small{The graph $\mathcal{P}(k,s,t)$}}
\end{figure}
\end{document}