Add exercice 1 td1 partie 2
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2 changed files with 116 additions and 72 deletions
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\maketitle
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\section{Exercice 1}
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\section{TD1 --- Partie 1}
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\paragraph{Graphe simple}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (2,0) {};
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\path (a) edge (b);
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\end{tikzpicture}
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\subsection{Exercice 1}
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\paragraph{Graphe multigraphe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (2,0) {};
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\path
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(a) [bend left] edge (b)
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(b) [bend left] edge (a)
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;
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\end{tikzpicture}
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\paragraph{Graphe simple}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (2,0) {};
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\path (a) edge (b);
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\end{tikzpicture}
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\paragraph{Graphe connexe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,1) {};
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\node(c)[state] at (2,0) {};
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\path
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(a) edge (b)
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(b) edge (c)
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(c) edge (a)
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;
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\end{tikzpicture}
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\paragraph{Graphe multigraphe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (2,0) {};
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\path
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(a) [bend left] edge (b)
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(b) [bend left] edge (a)
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;
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\end{tikzpicture}
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\paragraph{Graphe non connexe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,1) {};
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\node(c)[state] at (2,0) {};
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\path
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(a) edge (b)
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(b) edge (c)
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;
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\end{tikzpicture}
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\paragraph{Graphe connexe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,1) {};
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\node(c)[state] at (2,0) {};
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\path
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(a) edge (b)
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(b) edge (c)
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(c) edge (a)
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;
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\end{tikzpicture}
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\paragraph{Graphe complet}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,0) {};
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\node(c)[state] at (0,1) {};
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\node(d)[state] at (1,1) {};
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\path
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(a) edge (b)
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(a) edge (c)
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(a) edge (d)
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(b) edge (c)
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(b) edge (d)
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(c) edge (d)
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;
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\end{tikzpicture}
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\paragraph{Graphe non connexe}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,1) {};
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\node(c)[state] at (2,0) {};
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\path
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(a) edge (b)
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(b) edge (c)
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;
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\end{tikzpicture}
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\paragraph{Graphe biparti}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,0) {};
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\node(c)[state] at (0,1) {};
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\node(d)[state] at (1,1) {};
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\node(e)[state] at (2,0) {};
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\node(f)[state] at (2,1) {};
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\path
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(a) edge (b)
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(a) edge (c)
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(a) edge (d)
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(b) edge (c)
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(b) edge (d)
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(c) edge (d)
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(d) edge (e)
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(d) edge (f)
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(e) edge (f)
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;
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\end{tikzpicture}
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\paragraph{Graphe complet}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,0) {};
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\node(c)[state] at (0,1) {};
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\node(d)[state] at (1,1) {};
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\path
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(a) edge (b)
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(a) edge (c)
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(a) edge (d)
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(b) edge (c)
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(b) edge (d)
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(c) edge (d)
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;
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\end{tikzpicture}
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\paragraph{Graphe biparti}
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\begin{tikzpicture}[auto,x=2cm,y=2cm]
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\node(a)[state] at (0,0) {};
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\node(b)[state] at (1,0) {};
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\node(c)[state] at (0,1) {};
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\node(d)[state] at (1,1) {};
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\node(e)[state] at (2,0) {};
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\node(f)[state] at (2,1) {};
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\path
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(a) edge (b)
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(a) edge (c)
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(a) edge (d)
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(b) edge (c)
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(b) edge (d)
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(c) edge (d)
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(d) edge (e)
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(d) edge (f)
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(e) edge (f)
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;
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\end{tikzpicture}
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\section{TD1 --- Partie 2}
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\subsection{Exercice 1}
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Dans le graphe ci-dessous~:
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\includegraphics[width=\linewidth]{./img/td1-ex1.png}
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\begin{enumerate}
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\item Quels sont les successeurs de A, D et E~?
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A~: B, F \\
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B~: A, C, D, J \\
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E~: D, F
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\item Quels sont les prédécesseurs de B, C et F~?
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B~: A, C, D \\
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C~: B, D \\
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F~: A, E
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\item Est-ce qu'il y a des points qui n'ont pas de prédécesseur, ni successeur~?
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Lesquels~?
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G
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\item Quelle est l'extrémité initiale de l'arc $(A,B)$~?
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A
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\item Quelle est l'extrémité terminale de l'arc $(B,C)$~?
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C
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\item Est-ce qu'il y a des points qui ont à la fois l'extrémité initiale et terminale~?
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Lesquels~?
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A, B, C, D, E, F
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\end{enumerate}
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\end{document}
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theorie-graphes/img/td1-ex1.png
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theorie-graphes/img/td1-ex1.png
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