Merge pull request #1 from AndreasFMueller/master

update

9 files changed, 302 insertions, 0 deletions

diff --git a/buch/chapters/70-graphen/images/Makefile b/buch/chapters/70-graphen/images/Makefile
new file mode 100644
index 0000000..b42cbae
--- /dev/null
+++ b/buch/chapters/70-graphen/images/Makefile
@@ -0,0 +1,19 @@
+#
+# Makefile -- Bilder für Kapitel Graphen
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	peterson.pdf adjazenzu.pdf adjazenzd.pdf kreis.pdf
+
+peterson.pdf:	peterson.tex
+	pdflatex peterson.tex
+
+adjazenzu.pdf:	adjazenzu.tex
+	pdflatex adjazenzu.tex
+
+adjazenzd.pdf:	adjazenzd.tex
+	pdflatex adjazenzd.tex
+
+kreis.pdf:	kreis.tex
+	pdflatex kreis.tex
+
diff --git a/buch/chapters/70-graphen/images/adjazenzd.pdf b/buch/chapters/70-graphen/images/adjazenzd.pdf
new file mode 100644
index 0000000..dc3dd8f
--- /dev/null
+++ b/buch/chapters/70-graphen/images/adjazenzd.pdf
diff --git a/buch/chapters/70-graphen/images/adjazenzd.tex b/buch/chapters/70-graphen/images/adjazenzd.tex
new file mode 100644
index 0000000..5cef18e
--- /dev/null
+++ b/buch/chapters/70-graphen/images/adjazenzd.tex
@@ -0,0 +1,100 @@
+%
+% adjazenzd.tex -- Adjazenz-Matrix für einen gerichten Graphen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{mathtools}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math,calc}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\r{1.8}
+
+\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)});
+
+\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);
+
+\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) {$G$};
+
+\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] {$\scriptstyle 7$};
+
+
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=-1.1cm]
+\node at (0,0) [right] {$\displaystyle
+B(G)
+=
+\begin{pmatrix*}[r]
+-1& 0& 0& 0& 1&-1& 0\\
+ 1&-1& 0& 0& 0& 0&-1\\
+ 0& 1&-1& 0& 0& 1& 0\\
+ 0& 0& 1&-1& 0& 0& 1\\
+ 0& 0& 0& 1&-1& 0& 0
+\end{pmatrix*}$};
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=1.1cm]
+\node at (0,0) [right] {$\displaystyle
+A(G)
+=
+\begin{pmatrix*}[r]
+ 0& 1& 1& 0& 1\\
+ 1& 0& 1& 1& 0\\
+ 1& 1& 0& 1& 0\\
+ 0& 1& 1& 0& 1\\
+ 1& 0& 0& 1& 0
+\end{pmatrix*},
+\quad
+D(G)
+=
+\begin{pmatrix*}[r]
+3&0&0&0&0\\
+0&3&0&0&0\\
+0&0&3&0&0\\
+0&0&0&3&0\\
+0&0&0&0&1
+\end{pmatrix*}
+$};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/70-graphen/images/adjazenzu.pdf b/buch/chapters/70-graphen/images/adjazenzu.pdf
new file mode 100644
index 0000000..d3f255e
--- /dev/null
+++ b/buch/chapters/70-graphen/images/adjazenzu.pdf
diff --git a/buch/chapters/70-graphen/images/adjazenzu.tex b/buch/chapters/70-graphen/images/adjazenzu.tex
new file mode 100644
index 0000000..b6d129d
--- /dev/null
+++ b/buch/chapters/70-graphen/images/adjazenzu.tex
@@ -0,0 +1,98 @@
+%
+% adjazenzu.tex -- Adjazenz-Matrix für einen ungerichten Graphen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math,calc}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\r{1.8}
+
+\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)});
+
+\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);
+
+\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) {$G$};
+
+\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] {$\scriptstyle 7$};
+
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=-1.1cm]
+\node at (0,0) [right] {$\displaystyle
+B(G)
+=
+\begin{pmatrix}
+1&0&0&0&1&0&0\\
+1&1&0&0&0&1&0\\
+0&1&1&0&0&0&1\\
+0&0&1&1&0&1&0\\
+0&0&0&1&1&0&1
+\end{pmatrix}$};
+\end{scope}
+
+\begin{scope}[xshift=3cm,yshift=1.1cm]
+\node at (0,0) [right] {$\displaystyle
+A(G)
+=
+\begin{pmatrix}
+0&1&1&0&1\\
+1&0&1&1&0\\
+1&1&0&1&0\\
+0&1&1&0&1\\
+1&0&0&1&0
+\end{pmatrix},
+\quad
+D(G)
+=
+\begin{pmatrix}
+3&0&0&0&0\\
+0&3&0&0&0\\
+0&0&3&0&0\\
+0&0&0&3&0\\
+0&0&0&0&2
+\end{pmatrix}
+$};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/70-graphen/images/kreis.pdf b/buch/chapters/70-graphen/images/kreis.pdf
new file mode 100644
index 0000000..f7ed37a
--- /dev/null
+++ b/buch/chapters/70-graphen/images/kreis.pdf
diff --git a/buch/chapters/70-graphen/images/kreis.tex b/buch/chapters/70-graphen/images/kreis.tex
new file mode 100644
index 0000000..a926839
--- /dev/null
+++ b/buch/chapters/70-graphen/images/kreis.tex
@@ -0,0 +1,47 @@
+%
+% tikztemplate.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{mathtools}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\r{3}
+
+\foreach \w in {0,20,...,340}{
+	\draw (\w:\r) circle[radius=0.2];
+	\draw[->,shorten >= 0.2cm,shorten <= 0.2cm] (\w:\r) -- ({\w+20}:\r);
+}
+
+\foreach \x in {1,...,15}{
+	\node at ({20*(\x-1)}:\r) {$\scriptstyle \x$};
+}
+\node at (340:\r) {$\scriptstyle n$};
+\node at (320:\r) {$\scriptstyle \dots$};
+\node at (300:\r) {$\scriptstyle \dots$};
+
+\begin{scope}[xshift=4cm]
+\node at (0,0) [right] {$\displaystyle
+L=\begin{pmatrix*}[r]
+ 2&-1& 0& 0&\dots& 0&-1\\
+-1& 2&-1& 0&\dots& 0& 0\\
+ 0&-1& 2&-1&\dots& 0& 0\\
+ 0& 0&-1& 2&\dots& 0& 0\\
+\vdots&\vdots&\vdots&\vdots&\ddots&\vdots&\vdots\\
+ 0& 0& 0& 0&\dots& 2&-1\\
+-1& 0& 0& 0&\dots&-1& 2
+\end{pmatrix*}$};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/70-graphen/images/peterson.pdf b/buch/chapters/70-graphen/images/peterson.pdf
new file mode 100644
index 0000000..259d808
--- /dev/null
+++ b/buch/chapters/70-graphen/images/peterson.pdf
diff --git a/buch/chapters/70-graphen/images/peterson.tex b/buch/chapters/70-graphen/images/peterson.tex
new file mode 100644
index 0000000..c0af98b
--- /dev/null
+++ b/buch/chapters/70-graphen/images/peterson.tex
@@ -0,0 +1,38 @@
+%
+% tikztemplate.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\l{0.25}
+\def\r{1}
+\def\punkt#1{({\r*sin(((#1)-1)*72)},{\r*cos(((#1)-1)*72)})}
+\def\R{2}
+\def\Punkt#1{({\R*sin(((#1)-6)*72)},{\R*cos(((#1)-6)*72)})}
+\draw \Punkt{6} -- \Punkt{7} -- \Punkt{8} -- \Punkt{9} -- \Punkt{10} -- cycle;
+\draw \punkt{1} -- \punkt{3} -- \punkt{5} -- \punkt{2} -- \punkt{4} -- cycle;
+\foreach \k in {1,...,5}{
+	\draw \punkt{\k} -- \Punkt{(\k+5)};
+	\fill[color=white] \punkt{\k} circle[radius=\l];
+	\node at \punkt{\k} {$\k$};
+	\draw \punkt{\k} circle[radius=\l];
+}
+\foreach \k in {6,...,10}{
+	\fill[color=white] \Punkt{\k} circle[radius=\l];
+	\node at \Punkt{\k} {$\k$};
+	\draw \Punkt{\k} circle[radius=\l];
+}
+
+\end{tikzpicture}
+\end{document}
+