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author | LordMcFungus <mceagle117@gmail.com> | 2021-03-22 18:05:11 +0100 |
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committer | GitHub <noreply@github.com> | 2021-03-22 18:05:11 +0100 |
commit | 76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7 (patch) | |
tree | 11b2d41955ee4bfa0ae5873307c143f6b4d55d26 /buch/chapters/70-graphen/images | |
parent | more chapter structure (diff) | |
parent | add title image (diff) | |
download | SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.tar.gz SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.zip |
Merge pull request #1 from AndreasFMueller/master
update
Diffstat (limited to 'buch/chapters/70-graphen/images')
-rw-r--r-- | buch/chapters/70-graphen/images/Makefile | 19 | ||||
-rw-r--r-- | buch/chapters/70-graphen/images/adjazenzd.pdf | bin | 0 -> 23490 bytes | |||
-rw-r--r-- | buch/chapters/70-graphen/images/adjazenzd.tex | 100 | ||||
-rw-r--r-- | buch/chapters/70-graphen/images/adjazenzu.pdf | bin | 0 -> 21744 bytes | |||
-rw-r--r-- | buch/chapters/70-graphen/images/adjazenzu.tex | 98 | ||||
-rw-r--r-- | buch/chapters/70-graphen/images/kreis.pdf | bin | 0 -> 23540 bytes | |||
-rw-r--r-- | buch/chapters/70-graphen/images/kreis.tex | 47 | ||||
-rw-r--r-- | buch/chapters/70-graphen/images/peterson.pdf | bin | 0 -> 10833 bytes | |||
-rw-r--r-- | buch/chapters/70-graphen/images/peterson.tex | 38 |
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 Binary files differnew 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 Binary files differnew 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 Binary files differnew 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 Binary files differnew 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} + |