\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}

\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
\usepackage{braket} % needed for \Set
\usepackage{algorithm,algpseudocode}

\begin{document}
\begin{preview}
    \begin{algorithm}[H]
        \begin{algorithmic}
            \Require $G = (V, E)$ an undirected graph
            \State $n \gets |V|$
            \State Give all vertices an index $1 \leq i \leq n$ that defines an order

            \For{$i \in 1, \dots, n$}
                \State $v_i$.color $\gets 1$
            \EndFor
            \\
            \For{$i \in 1, \dots, n$}
                \For{$j \in i+1, \dots, n$}
                    \If{$\Set{v_i, v_j} \in E \land v_i.\text{color} = v_j.\text{color}$}
                        \State $v_j.color \gets v_j.color + 1$
                    \EndIf
                \EndFor
            \EndFor
        \end{algorithmic}
    \caption{Find a vertex coloring for $G$}
    \label{alg:vertexColoring}
    \end{algorithm}
\end{preview}
\end{document}