https://davidvajda.de/david4/2024-02-24 ... lvenus.tex
https://davidvajda.de/david4/2024-02-24 ... lvenus.pdf
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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz,german,graphicx}
\usepackage[landscape=true]{geometry}
\usetikzlibrary{circuits.logic.IEC, positioning}
\usetikzlibrary{arrows , automata , positioning}
\usepackage[utf8]{inputenc}
\begin{document}
\section{David are two graphes}
\begin{center}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2.5cm]
%Knoten
\node (1) [state, thick] {1};
\node (2) [state, thick, below of= 1, right of= 1] {2};
\node (3) [state, thick, below of= 2] {3};
\node (4) [state, thick, below of= 3, left of= 3] {4};
\node (5) [state, thick, below of= 1, left of = 1] {5};
\node (6) [state, thick, below of= 5] {6};
%Verbindungen
\path[thick,->]
(1) edge (6)
(1) edge (3)
(3) edge (6)
(4) edge (5)
(4) edge (2)
(5) edge (2)
;
\end{tikzpicture}
\end{center}
\section{David and Cyclohexan}
\begin{center}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2.5cm]
%Knoten
\node (1) [state, thick] {1};
\node (2) [state, thick, below of= 1, right of= 1] {2};
\node (3) [state, thick, below of= 2] {3};
\node (4) [state, thick, below of= 3, left of= 3] {4};
\node (5) [state, thick, below of= 1, left of = 1] {5};
\node (6) [state, thick, below of= 5] {6};
%Verbindungen
\path[thick,->]
(1) edge (6)
(1) edge (3)
(3) edge (6)
(4) edge (5)
(4) edge (2)
(5) edge (2)
(1) edge (2)
(2) edge (3)
(3) edge (4)
(4) edge (6)
(6) edge (5)
(5) edge (1)
;
\end{tikzpicture}
\end{center}
\section{But Cyclohexan is another Graph because of the edges}
\begin{center}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2.5cm]
%Knoten
\node (1) [state, thick] {1};
\node (2) [state, thick, below of= 1, right of= 1] {2};
\node (3) [state, thick, below of= 2] {3};
\node (4) [state, thick, below of= 3, left of= 3] {4};
\node (5) [state, thick, below of= 1, left of = 1] {5};
\node (6) [state, thick, below of= 5] {6};
%Verbindungen
\path[thick,->]
(1) edge (2)
(2) edge (3)
(3) edge (4)
(4) edge (6)
(6) edge (5)
(5) edge (1)
;
\end{tikzpicture}
\end{center}
\section{Venus}
\begin{center}
\begin{tikzpicture}[>=stealth',shorten >=1pt,auto,node distance=2.5cm]
%Knoten
\node (1) [state, thick] {1};
\node (2) [state, thick, below of= 1, right of= 1] {2};
\node (3) [state, thick, below of= 2] {3};
\node (5) [state, thick, below of= 1, left of = 1] {5};
\node (6) [state, thick, below of= 5] {6};
%Verbindungen
\path[thick,->]
(5) edge (2)
(2) edge (6)
(6) edge (1)
(1) edge (3)
(3) edge (5)
;
\end{tikzpicture}
\end{center}
\section{David is isomorphism, is bijektive projection}
$$
G = (V,E)
$$
$$
G'=(V',E')
$$
Bijektive Abbildungen sind ebenso Teil der Graphentheorie nicht nur die Graphen selber
\end{document}