\documentclass[a4paper,12pt]{report} 
\usepackage{tikz,amsmath,subcaption} 
\usepackage[labelsep=endash]{caption}
\usepackage[labelsep=endash]{caption}
\usepackage{tikz,amsmath,subcaption} 
\usepackage[labelsep=endash]{caption}
\usepackage{xepersian} 
\settextfont{Yas} 
\tikzstyle{vertex}=[] 
\newcommand{\vertex}{\node[vertex]} 
\tikzstyle{vertexa}=[circle, draw, inner sep=0pt, minimum size=15pt]  
\newcommand{\vertexa}{\node[vertexa]} 


  \begin{figure}
\begin{subfigure}{}


\centering
\[
\begin{tikzpicture}[near end,scal=.02]

\draw (0,4) --  (16,4) node[left,above]{$a_3$     $a_1$   $a_2$    $a_4$    $b_1$    $a_5$    $b_2$    $b_3$  $b_4$  $a_7$  $a_6$  $a_8$  $b_5$  $b_6$  $a_9$  $b_7$  $b_8$  $a_{10}$  $b_9$  $a_{11}$  $b_{10}$  $a_{12}$  $b_{11}$  $a_{14}$  $b_{12}$  $a_{15}$  $a_{13}$  $b_{13}$  $b_{14}$ $b_{15}$};
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 \vertex (b2) at (2.5,3.3) []{}; 
 \vertex (b3) at (4,3.8) []{}; 
    \vertex (b4) at (3.5,3.2)[ ]{}; 
 \vertex (b5) at (6.5,3) []{}; 
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\draw (0,0) -- (16,0) node[below]{$c_1d_1c_3c_2c_4d_2c_6d_3c_5d_4c_9d_6c_7d_7d_5c_{11}c_8c_{12}d_9d_8c_{10}d_{10}d_{12}c_{13}d_{11}c_{14}d_{14}d_{13}c_{15}d_{15}$}; 
\end{tikzpicture}

\end{document}