diff options
Diffstat (limited to 'buch/chapters')
| -rw-r--r-- | buch/chapters/70-graphen/images/Makefile | 5 | ||||
| -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 | 19952 -> 21744 bytes | |||
| -rw-r--r-- | buch/chapters/70-graphen/images/adjazenzu.tex | 27 |
5 files changed, 123 insertions, 9 deletions
diff --git a/buch/chapters/70-graphen/images/Makefile b/buch/chapters/70-graphen/images/Makefile index 9e61446..529f314 100644 --- a/buch/chapters/70-graphen/images/Makefile +++ b/buch/chapters/70-graphen/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: peterson.pdf adjazenzu.pdf +all: peterson.pdf adjazenzu.pdf adjazenzd.pdf peterson.pdf: peterson.tex pdflatex peterson.tex @@ -11,3 +11,6 @@ peterson.pdf: peterson.tex adjazenzu.pdf: adjazenzu.tex pdflatex adjazenzu.tex +adjazenzd.pdf: adjazenzd.tex + pdflatex adjazenzd.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 differindex c24335a..d3f255e 100644 --- a/buch/chapters/70-graphen/images/adjazenzu.pdf +++ 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 index 29e094f..b6d129d 100644 --- a/buch/chapters/70-graphen/images/adjazenzu.tex +++ b/buch/chapters/70-graphen/images/adjazenzu.tex @@ -46,13 +46,13 @@ \node at (E) {$5$}; \node at (0,0) {$G$}; -\node at ($0.5*(A)+0.5*(B)$) [above right] {$1$}; -\node at ($0.5*(B)+0.5*(C)$) [above left] {$2$}; -\node at ($0.5*(C)+0.5*(D)$) [left] {$3$}; -\node at ($0.5*(D)+0.5*(E)$) [below] {$4$}; -\node at ($0.5*(E)+0.5*(A)$) [below right] {$5$}; -\node at ($0.6*(A)+0.4*(C)$) [above] {$6$}; -\node at ($0.4*(B)+0.6*(D)$) [left] {$7$}; +\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} @@ -79,7 +79,18 @@ A(G) 1&1&0&1&0\\ 0&1&1&0&1\\ 1&0&0&1&0 -\end{pmatrix}$}; +\end{pmatrix}, +\quad +D(G) += +\begin{pmatrix} +3&0&0&0&0\\ +0&3&0&0&0\\ +0&0&3&0&0\\ +0&0&0&3&0\\ +0&0&0&0&2 +\end{pmatrix} +$}; \end{scope} \end{tikzpicture} |