From 972eba4c4cb38eb330bd053500e627085a3f4328 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Fri, 12 Mar 2021 17:27:08 +0100
Subject: add new slides

---
 vorlesungen/slides/8/graph.tex | 117 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 117 insertions(+)
 create mode 100644 vorlesungen/slides/8/graph.tex

(limited to 'vorlesungen/slides/8/graph.tex')

diff --git a/vorlesungen/slides/8/graph.tex b/vorlesungen/slides/8/graph.tex
new file mode 100644
index 0000000..32150af
--- /dev/null
+++ b/vorlesungen/slides/8/graph.tex
@@ -0,0 +1,117 @@
+%
+% graph.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Graph}
+\vspace{-18pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\def\r{2.4}
+
+\begin{scope}
+\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)});
+\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)});
+\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)});
+\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)});
+\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)});
+
+\uncover<3->{
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C);
+	\draw[color=white,line width=5pt] (B) -- (D);
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (D);
+
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (B);
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (B) -- (C);
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (C) -- (D);
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (D) -- (E);
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm] (E) -- (A);
+}
+
+\uncover<2->{
+	\draw (A) circle[radius=0.2];
+	\draw (B) circle[radius=0.2];
+	\draw (C) circle[radius=0.2];
+	\draw (D) circle[radius=0.2];
+	\draw (E) circle[radius=0.2];
+
+	\node at (A) {$1$};
+	\node at (B) {$2$};
+	\node at (C) {$3$};
+	\node at (D) {$4$};
+	\node at (E) {$5$};
+}
+\node at (0,0) {$G$};
+
+\uncover<3->{
+	\node at ($0.5*(A)+0.5*(B)-(0.1,0.1)$)
+		[above right] {$\scriptstyle 1$};
+	\node at ($0.5*(B)+0.5*(C)+(0.05,-0.07)$)
+		[above left] {$\scriptstyle 2$};
+	\node at ($0.5*(C)+0.5*(D)+(0.05,0)$)
+		[left] {$\scriptstyle 3$};
+	\node at ($0.5*(D)+0.5*(E)$)
+		[below] {$\scriptstyle 4$};
+	\node at ($0.5*(E)+0.5*(A)+(-0.1,0.1)$)
+		[below right] {$\scriptstyle 5$};
+	\node at ($0.6*(A)+0.4*(C)$)
+		[above] {$\scriptstyle 6$};
+	\node at ($0.4*(B)+0.6*(D)$)
+		[left] {$\scriptstyle 7$};
+}
+
+\uncover<8->{
+	\draw[shorten >= 0.2cm,shorten <= 0.2cm]
+		(E) to[out=-18,in=-126,distance=2cm] (E);
+
+	\draw[color=red,line width=4pt] ($(E)+(-0.5,-0.5)+(0,-0.5)$)
+		-- ($(E)+(0.5,0.5)+(0,-0.5)$);
+	\draw[color=red,line width=4pt] ($(E)+(-0.5,0.5)+(0,-0.5)$)
+		-- ($(E)+(0.5,-0.5)+(0,-0.5)$);
+}
+
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Definition}
+Ein Graph $G=(V,E)$ ist
+\begin{enumerate}
+\item<2->
+Eine Menge $V$ von Knoten (Vertizes):
+$V=\{v_1,v_2,\dots\}$
+\item<3->
+Eine Menge $E$ von Kanten (Edges):
+\[
+E\subset
+\left\{ e = \{v_1,v_2\}\;\left|\; \begin{minipage}{1.3cm}\raggedright
+$v_i\in V$\\
+$v_1\ne v_2$
+\end{minipage}
+\right.
+\right\}
+\]
+\end{enumerate}
+\end{block}
+\vspace{-20pt}
+\uncover<5->{%
+\begin{block}{Achtung:}
+\begin{itemize}
+\item<6-> Kanten sind Mengen
+\uncover<7->{$\Rightarrow$ zwei verschiedene Knoten}
+\uncover<8->{$\Rightarrow$ Keine Schleifen}
+\item<9-> Kanten sind ungerichtet, keine ``Einbahnstrassen''
+\end{itemize}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
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