119 lines
3.2 KiB
TeX
119 lines
3.2 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{ngerman}
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\usepackage{float}
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\usepackage{diagbox}
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\usepackage[utf8]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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\usepackage{tikz}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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\def \pname {Marvin Herrmann} %
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\def \pmatrikel {108018265436} %
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\def \gruppe {2 (Mi 10-12 Andre)}
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\def \qname {Pascal Brackmann}
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\def \qmatrikel {108017113834} %
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\def \uebung {4} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
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\noindent \pmatrikel \quad \pname \\
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\noindent \qmatrikel \quad \qname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe 4.3}
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\begin{enumerate}[1.]
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\item Graph $G=(V,E)$ mit\\
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Knotenmenge: $V=\{1,2,3,4,5,6\}$\\
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Kantenmenge: $E=
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\{
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(1,2),
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(1,3),
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(2,3),
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(3,4),
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(4,5),
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(5,6),
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(6,4)
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\}$
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\\
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Adjazenz-Matrix:\\
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\begin{tabular}{c|cccccc}
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& 1 & 2 & 3 & 4 & 5 & 6 \\
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\hline
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1 & 0 & 1 & 1 & 0 & 0& 0 \\
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2 & 0 & 0 & 1 & 0 & 0& 0 \\
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3 & 0 & 0 & 0 & 1 & 0& 0 \\
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4 & 0 & 0 & 0 & 0 & 1& 0 \\
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5 & 0 & 0 & 0 & 0 & 0& 1 \\
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6 & 0 & 0 & 0 & 1 & 0& 0 \\
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\end{tabular}
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\\
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Inzidenz-Matrix:\\
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\begin{tabular}{c|ccccccc}
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1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\
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2 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\
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3 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\
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4 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\
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5 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\
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6 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\
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\end{tabular}
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\item \begin{tikzpicture}
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\def \n {5}
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\def \radius {3cm}
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\def \margin {8} % margin in angles, depends on the radius
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\node[draw, circle] (1) at (0,1) {1};
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\node[draw, circle] (4) at (2,2) {4};
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\node[draw, circle] (6) at (2,0) {6};
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\node[draw, circle] (3) at (1,0) {3};
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\draw [->]
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(1) edge (3)
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(3) edge (4)
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(6) edge (4);
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\end{tikzpicture}
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\\
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$V'=\{1,3,4,6\}$
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\item \begin{tikzpicture}
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\def \n {5}
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\def \radius {3cm}
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\def \margin {8} % margin in angles, depends on the radius
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\node[draw, circle] (1) at (0,0) {1};
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\node[draw, circle] (3) at (1,0) {3};
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\node[draw, circle] (4) at (2,0) {4};
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\node[draw, circle] (5) at (3,0) {5};
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\draw [->]
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(1) edge (3)
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(3) edge (4)
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(4) edge (5);
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\end{tikzpicture}
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\\
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$V'=\{1,3,4,5\}$
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\end{enumerate}
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\end{document}
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