130 lines
3.5 KiB
TeX
130 lines
3.5 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 4.2}
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\begin{enumerate}[1.]
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\item Graph $G=(V,E)$ mit\\
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Knotenmenge: $V=\{a,b,c,d,e,f\}$\\
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Kantenmenge: $E=
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\{
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\{a,b\},
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\{a,c\},
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\{a,d\},
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\{a,f\},
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\{b,f\},
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\{b,e\},
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\{c,d\},
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\{d,e\}
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\}
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$
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\\
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Adjazenz-Matrix:\\
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\begin{tabular}{c|ccccccc}
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& a & b & c & d & e & f \\
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\hline
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a & 0 & 1 & 1 & 1 & 0 & 1 \\
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b & 1 & 0 & 0 & 0 & 1 & 1 \\
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c & 1 & 0 & 0 & 1 & 0 & 0 \\
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d & 1 & 0 & 1 & 0 & 1 & 0 \\
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e & 0 & 1 & 0 & 1 & 0 & 0 \\
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f & 1 & 1 & 0 & 0 & 0 & 0 \\
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\end{tabular}
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\\
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\\
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Inzidenz-Matrix:\\
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\begin{tabular}{c|ccccccccc}
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a & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\
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b & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\
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c & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\
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d & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 \\
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e & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\
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f & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\
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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] (a) at (3,2) {a};
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\node[draw, circle] (b) at (1,1) {b};
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\node[draw, circle] (c) at (2,1) {c};
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\node[draw, circle] (d) at (3,1) {d};
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\node[draw, circle] (f) at (4,1) {f};
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\node[draw, circle] (e) at (0,0) {e};
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\draw (a)--(b);
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\draw (a)--(c);
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\draw (a)--(d);
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\draw (a)--(f);
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\draw (b)--(e);
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\end{tikzpicture}
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\\
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$G \setminus \{\{b,f\},\{c,d\},\{d,e\}\}$
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\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] (b) at (2,2) {b};
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\node[draw, circle] (a) at (1,1) {a};
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\node[draw, circle] (f) at (2,1) {f};
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\node[draw, circle] (e) at (3,1) {e};
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\node[draw, circle] (c) at (0,0) {c};
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\node[draw, circle] (d) at (2,0) {d};
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\draw (b)--(a);
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\draw (b)--(f);
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\draw (b)--(e);
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\draw (a)--(c);
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\draw (a)--(d);
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\end{tikzpicture}
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\\
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$G \setminus \{\{a,f\},\{c,d\},\{d,e\}\}$
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\end{enumerate}
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\end{document}
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