Table des matières (masquer)

  1. 1. Graphes
  2. 2. Arbres

1.  Graphes

Le célèbre graphe des sept ponts de Konigsberg 

\usepackage{pst-node}

\psset{fillcolor=blue,fillstyle=solid}
\begin{psmatrix}[mnode=circle,rowsep=0.8]
   & {}      \\
{} &    & {} \\
   & {} & 
\end{psmatrix}

\ncline{2,1}{2,3}
\ncline{1,2}{2,3}
\ncline{3,2}{2,3}
\ncarc[arcangle=60] {2,1}{1,2}
\ncarc[arcangle=-20]{2,1}{1,2}
\ncarc[arcangle=60] {3,2}{2,1}
\ncarc[arcangle=-20]{3,2}{2,1}

Un graphe pondéré pour un problème de probabilités 

\usepackage{pst-node}

\begin{psmatrix}[mnode=circle,colsep=3]
A & B \\
\end{psmatrix}

\psset{arrows=->,shortput=nab}

\ncarc[arcangle=20]{1,1}{1,2}^{0.6}
\nccircle[angleA=-90]{1,2}{0.5}_{0.4}
\ncarc[arcangle=20]{1,2}{1,1}^{0.7}
\nccircle[angleA=90]{1,1}{0.5}_{0.3}

Un diagramme commutatif 

\usepackage{pst-node}

\begin{psmatrix}
$G$ & $\mathrm{im}(f)$ \\
$G/\ker(f)$
\end{psmatrix}

\psset{arrows=->,shortput=nab,nodesep=5pt}
\ncline{1,1}{1,2}^{$f$}
\ncline{1,1}{2,1}_{$\varphi$}
\ncline[linestyle=dashed]{2,1}{1,2}_{$h$}

2.  Arbres

Un arbre relativement simple 

\usepackage{pst-tree}

\pstree{\Tp}{%
  \pstree{\TC*}{\TC* \TC}
  \pstree{\TC }{
	\pstree{\TC*}{\TC* \TC}
	\pstree{\TC }{\TC* \TC}}
}

Un schéma de Bernoulli nettement plus élaboré 

\usepackage{pst-tree}


\psset{levelsep=1cm}
\pstree[edge=none]{\Tp}{%
	\pstree{\TR{Épreuve 1}}{
		\pstree{\TR{Épreuve 2}}{
			\TR{Épreuve 3}
		}
	}
} 
\quad 
\pstree{\Tp}{%
  \pstree{\Tc*{3pt}}{
	\pstree{\Tc*{3pt}}{\Tc*{3pt} \Tc{3pt}~{$\frac18$}}
	\pstree{\Tc{3pt}}{\Tc*{3pt} \Tc{3pt}~{$\frac18$}}}
  \pstree{\Tc{3pt}~[tnpos=r]{$\frac12$}}{
	\pstree{\Tc*{3pt}~[tnpos=l]{$\frac14$}}{\Tc*{3pt} \Tc{3pt}~{$\frac18$}}
	\pstree{\Tc{3pt}}{\Tc*{3pt} \Tc{3pt}~{$\frac18$}}}
}