\documentclass[a4paper,11pt]{article}

\usepackage{ngerman}
\usepackage{amsmath,amsfonts,amssymb,amsthm}

\usepackage{tikz}
\usetikzlibrary{arrows,chains,matrix,positioning,scopes}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{math}

\def\O{\mathcal{O}}
\def\sort{\mathrm{sort}}
\def\scan{\mathrm{scan}}
\def\dist{\mathrm{dist}}
\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\E{\mathbb{E}}


\begin{document}


\textbf{Aufgabe 3}
\begin{center}
	\begin{tikzpicture}[scale=0.8,every node/.style={circle,inner sep=1mm,minimum size=2mm}]
	\node[draw,circle]      at (0, 0)       (v1) {};
	\node[draw,circle]      at (2, 0)       (v2) {};
	\node[draw,circle]      at (4, 0)       (v3) {};
	\node[draw,circle,fill] at (1.5, 0.816) (v4) {};
	\node[draw,circle,fill] at (2.5, 0.816) (v5) {};
	\node[draw,circle]      at (1, 1.732)   (v6) {};
	\node[draw,circle,fill] at (2, 1.732)   (v7) {};
	\node[draw,circle]      at (3, 1.732)   (v8) {};
	\node[draw,circle]      at (2, 3.464)   (v9) {};
	
	\tikzstyle{every node}=[pos=0.5,above,scale=0.8,font=\small] 
	\draw (v1) -- (v2)  node{};
	\draw (v1) -- (v6)  node{};
	\draw (v2) -- (v3)  node{};
	\draw (v2) -- (v4)  node{};
	\draw (v2) -- (v5)  node{};
	\draw (v3) -- (v8)  node{};
	\draw (v4) -- (v5)  node{};
	\draw (v4) -- (v6)  node{};
	\draw (v4) -- (v7)  node{};
	\draw (v5) -- (v7)  node{};
	\draw (v5) -- (v8)  node{};
	\draw (v6) -- (v7)  node{};
	\draw (v6) -- (v9)  node{};
	\draw (v7) -- (v8)  node{};
	\draw (v8) -- (v9)  node{};
	\end{tikzpicture}  
\end{center}


\textbf{Aufgabe 4}
\begin{center}
	\begin{tikzpicture}[scale=0.8,every node/.style={circle,inner sep=1mm,minimum size=2mm}]
	\node[draw,circle] at (0, 2.4) (a) {};
	\node[draw,circle] at (1, 3.4) (b) {};
	\node[draw,circle] at (2.4, 3.4) (c) {};
	\node[draw,circle] at (3.4, 2.4) (d) {};
	\node[draw,circle] at (3.4, 1) (e) {};
	\node[draw,circle] at (2.4, 0) (f) {};
	\node[draw,circle] at (1, 0) (g) {};
	\node[draw,circle] at (0, 1) (h) {};
	
	\path[-,>=triangle 60,shorten >=0pt,every node/.style={font=\small}]
	(a) edge node () {} (b)
	(c) edge node () {} (d)
	(e) edge node () {} (f)
	(g) edge node () {} (h)
	(b) edge node () {} (g)
	(c) edge node () {} (f)
	(a) edge node () {} (d)
	(h) edge node () {} (e)
	;
	\end{tikzpicture}
\end{center}


\end{document}