Re: Graphs

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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}