\documentclass{report}
  \usepackage{tikz}
  \usetikzlibrary{calc}
  \begin{document}
  \[
  \begin{tikzpicture}
  \vertex (a1) at (0,0) []{};
  \vertex (a2) at (1,0) []{};
  \vertex (a3) at (2,0) []{};
  \vertex (a4) at (3,0) []{};
  \vertex (b1) at (-1,-1.5) []{};
  \vertex (b2) at (0,-1.5) []{};
  \vertex (b3) at (1,-1.5) []{};
  \vertex (b4) at (2,-1.5) []{};
  \vertex (b5) at (3,-1.5) []{};
  \vertex (b6) at (4,-1.5) []{};
  
  \path  
  (a1) edge (b1)
  (a1) edge (b2)
  (a1) edge (b4)
  (a2) edge (b2)
  (a2) edge (b3)
  (a2) edge (b5)
  (a3) edge (b1)
  (a3) edge (b5)
  (a3) edge (b6)
  (a4) edge (b3)
  (a4) edge (b4)
  (a4) edge (b5);
  \end{tikzpicture}
  \]
   \end{document}