# How do I draw this decomposition in LaTex?

I am currently learning how to use Tikz in order to draw graphs. Since I am a beginner I can't seem to figure out how to draw the following graph:

What's puzzling me here is the shapes encircling the graph vertices as well as the alignment of text underneath those shapes.

Here is my code so far (it only generates L0 and L1):

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=2]
\tikzset{vertex/.style={draw, circle, inner sep = 2pt, fill=black}}
\node (v2) at (0,0.5) [vertex] {};
\node (v3) at (.5,1) [vertex] {};
\node (v5) at (.5, .5) [vertex] {};
\node (v6) at (.5, 0) [vertex] {};
\draw (v2) to (v3);
\draw (v2) to (v5);
\draw (v2) to (v6);
\end{tikzpicture}
\end{document}


• Welcome to TeX.SE! Can you please show us the code you have so far? Nov 11, 2021 at 22:32
• @Mensch I will add it but it is not much. Nov 11, 2021 at 22:37

Technically the code you provided is all you need. But if if you want to draw trees you may want to use the child {} command

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{nicefrac,xfrac}
\tikzset{vertex/.style={draw, circle, inner sep = 1pt, fill=black,}}
\begin{document}
\begin{tikzpicture}[grow=0,level 1/.style={sibling distance=3em},
level 2/.style={sibling distance=2em},]
\node[vertex] (z) {}
child { node[vertex] (x){}
child { node[vertex] (y) {} }
child { node[vertex] {} }
}
child { node[vertex] {}
child { node[vertex] (a) {} }
child { node[vertex] (b) {} }
}
child {node[vertex] {}
child { node[vertex] {} }
child { node[vertex] {} }
};
%ellipse
\draw[violet] (0,0) ellipse (0.1cm and 0.5cm);
\draw[violet] (1.5,0) ellipse (0.25cm and 1.5cm);
\draw[violet] (3,0) ellipse (0.5cm and 2cm);

\node[vertex,right of=a, xshift=2cm] (c) {};
\node[vertex,right of=b, xshift=2cm] (d) {};

\draw[dotted] (c) -- (a);
\draw[dotted] (d) -- (b);
\path [bend right] (c) edge (d);

%labels
\node at (0,-3)  {$L_{0}$};
\node at (1.5,-3)  {$L_{1}$};
\node at (3,-3)  {$L_{2}$};
\node at (6,-3)  {$L_{\tfrac{K-1}{2}}$};

\end{tikzpicture}
\end{document}