Merge pull request #1 from AndreasFMueller/master

update

1 files changed, 164 insertions, 0 deletions

diff --git a/vorlesungen/slides/8/inzidenzd.tex b/vorlesungen/slides/8/inzidenzd.tex
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+++ b/vorlesungen/slides/8/inzidenzd.tex
@@ -0,0 +1,164 @@
+%
+% inzidenzd.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Inzidenz- und Adjazenz-Matrix}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.40\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\r{2.2}
+
+\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)});
+
+\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (A) -- (C);
+\draw[color=white,line width=5pt] (B) -- (D);
+{\color<2->{darkgreen}
+\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);
+
+\draw (A) circle[radius=0.2];
+\only<-2>{
+\fill[color=white] (B) circle[radius=0.2];
+}
+\only<3->{
+\fill[color=red!20] (B) 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) {$G$};
+
+\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] {$\scriptstyle 6$};
+{\color<2->{darkgreen}
+\node at ($0.4*(B)+0.6*(D)$) [left] {$\scriptstyle 7$};
+}
+
+\end{tikzpicture}
+\end{center}
+\vspace{-15pt}
+\uncover<5->{%
+\begin{block}{Definition}
+\vspace{-20pt}
+\begin{align*}
+B(G)_{ij}&=-1&&\Leftrightarrow&&\text{Kante $j$ von $i$}\\
+B(G)_{kj}&=+1&&\Leftrightarrow&&\text{Kante $j$ nach $k$}\\
+A(G)_{ij}&=\phantom{-}1&&\Leftrightarrow&&\text{Kante von $i$ nach $j$}
+\end{align*}
+\end{block}}
+\end{column}
+\begin{column}{0.58\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\dx{0.84}
+\def\dy{0.48}
+
+\begin{scope}[xshift=4cm,yshift=3cm]
+\uncover<3->{
+\fill[color=red!20] 
+({-0.67-(7-1)*\dx-0.4},{-0.38-(2-1)*\dy-0.2})
+rectangle
+({-0.67-(7-7)*\dx+0.2},{-0.38-(2-1)*\dy+0.16});
+}
+\uncover<2->{
+\fill[color=darkgreen!40,opacity=0.5] 
+({-0.67-(7-7)*\dx-0.4},{-0.38-(5-1)*\dy-0.2})
+rectangle
+({-0.67-(7-7)*\dx+0.2},{-0.38-(1-1)*\dy+0.16});
+}
+%\draw (0,0) circle[radius=0.05];
+\foreach \x in {1,...,7}{
+	\node[color=gray] at ({-0.67-(7-\x)*\dx},0.0) {\tiny $\x$};
+}
+\draw[color=gray] ({-0.72-6*\dx},-0.1) -- (-0.6,-0.1);
+\foreach \y in {1,...,5}{
+	\node[color=gray] at ({0},{-0.38-(\y-1)*\dy}) {\tiny $\y$};
+}
+\draw[color=gray] (-0.1,-0.28) -- (-0.1,-2.4);
+\node[color=gray] at ({-0.67-(7-4)*\dx},0.04) [above] {\tiny Kanten};
+\node[color=gray] at ({0.00},{-0.38-(3-1)*\dy})
+	[above,rotate=-90] {\tiny Knoten};
+\end{scope}
+
+\uncover<4->{
+\begin{scope}[xshift=2.32cm,yshift=-0.24cm]
+%\draw (0,0) circle[radius=0.05];
+\fill[color=red!20] 
+({-0.67-(5-1)*\dx-0.4},{-0.38-(2-1)*\dy-0.2})
+rectangle
+({-0.67-(5-5)*\dx+0.2},{-0.38-(2-1)*\dy+0.16});
+\fill[color=red!20] 
+({-0.67-(5-2)*\dx-0.4},{-0.38-(5-1)*\dy-0.2})
+rectangle
+({-0.67-(5-2)*\dx+0.2},{-0.38-(1-1)*\dy+0.16});
+\foreach \x in {1,...,5}{
+	\node[color=gray] at ({-0.67-(5-\x)*\dx},0.0) {\tiny $\x$};
+}
+\draw[color=gray] ({-0.72-4*\dx},-0.1) -- (-0.6,-0.1);
+\foreach \y in {1,...,5}{
+	\node[color=gray] at ({0},{-0.38-(\y-1)*\dy}) {\tiny $\y$};
+}
+\draw[color=gray] (-0.1,-0.28) -- (-0.1,-2.4);
+\node[color=gray] at ({-0.67-(5-3)*\dx},0.04) [above] {\tiny Knoten};
+\node[color=gray] at ({0.00},{-0.38-(3-1)*\dy})
+	[above,rotate=-90] {\tiny Knoten};
+\end{scope}
+}
+
+\node at (0,0) {$\displaystyle
+\begin{aligned}
+B(G)
+&=
+\begin{pmatrix*}[r]
+-1& 0& 0& 0&+1&-1& 0\\
++1&-1& 0& 0& 0& 0&-1\\
+ 0&+1&-1& 0& 0&+1& 0\\
+ 0& 0&+1&-1& 0& 0&+1\\
+ 0& 0& 0&+1&-1& 0& 0
+\end{pmatrix*}
+\\[20pt]
+\uncover<4->{
+A(G)
+&=
+\begin{pmatrix*}[r]
+ 0&\phantom{-}1&\phantom{-}1& 0&\phantom{-}1\\
+\phantom{-}1& 0&\phantom{-}1&\phantom{-}1& 0\\
+\phantom{-}1&\phantom{-}1& 0&\phantom{-}1& 0\\
+ 0&\phantom{-}1&\phantom{-}1& 0&\phantom{-}1\\
+\phantom{-}1& 0& 0&\phantom{-}1& 0
+\end{pmatrix*}}
+\end{aligned}$};
+\end{tikzpicture}
+\end{center}
+\end{column}
+\end{columns}
+\end{frame}