tkz-berge.sty - Graph Theory

The package tkz-berge.sty is a collection of some useful macros if you want to draw some classic graphs of the graph theory or to make others graphs.

Why tkz-berge.sty ?

Claude Berge (1926 – 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory. He played a major role in the renaissance of combinatorics and he is remembered for his famous conjecture on perfect graphs, solved some months after his death.

The names of graphs can be found here MathWorld by E.Weisstein
mathworld.wolfram.com
Graph Theory In Latex by Rafael Villarroel
Fauskes.net by Kjell Magne Fauskes You can find the following graphs in this document : NamedGraphs.pdf

Groetzsh-II graph

Heawood graph : [PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc} 
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\tikzstyle{VertexStyle} = [shape           = circle,
                           shading         = ball,
                           ball color      = blue!60,
                           inner sep       = 6pt,
                           draw]
\SetVertexNoLabel
\tikzstyle{EdgeStyle}    = [thick,double= red,
                            double distance = 1pt] 
\begin{tikzpicture}[rotate=-18]
 \draw[scale=.5,samples at={-6.4,-6.3,...,6.4},
       smooth,thick,
       variable=\t,
       double= red,
       double distance = 1pt]
       plot ({3*(1.5*cos(\t r) +3*cos(1.5*\t r))},%
             {3*(1.5*sin(\t r) -3*sin(1.5*\t r))});
\begin{scope}[rotate=36]
   \grStar[prefix=a,RA=2.2]{6}%
   \grEmptyCycle[prefix=b,RA=4.4]{5}%
\end{scope}
\end{tikzpicture}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Circulant graph

Circulant graph:[PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc} 
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\begin{center}
\begin{tikzpicture}
\GraphInit[vstyle=Shade]
\grCirculant[Math,RA=6]{12}{5}
\end{tikzpicture}
\end{center}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Complete graph

Its order is 16 and it is possible to build it with a circulant graph.

Circulant et Complet graph : [PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc} 
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\begin{center}
\begin{tikzpicture}
  \renewcommand*{\VertexBallColor}{green!50!black}
  \GraphInit[vstyle=Art]
  \grComplete[RA=6]{16}
\end{tikzpicture}
\end{center}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Dodecahedral : a Platonic graph

Platonic-Dodecahedral graph : [PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc} 
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\begin{center}
\begin{tikzpicture}
  \SetVertexNoLabel
  \GraphInit[vstyle=Shade]
  \SetGraphShadeColor{green!60!black!30}{Brown}{white}
  \grDodecahedral[RA=7,RB=4.5]
\end{tikzpicture}
\end{center}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Möbius-Kantor graph

MobiusKantor graph : [PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\begin{center}
\begin{tikzpicture}
   \tikzstyle{VertexStyle}=[shape        = circle,
                            shading      = ball,
                            ball color   = green!40!black,
                            minimum size = 24pt,
                            draw]
   \SetVertexNoLabel
   \tikzstyle{EdgeStyle}= [thick,
                           double = orange,
                           double distance = 1pt]
   \grMobiusKantor[RA=5]
\end{tikzpicture}
\end{center}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Petersen generalized graph

Petersen graph :[PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\begin{center}
\begin{tikzpicture}[rotate=90]
\tikzstyle{VertexStyle} = [shape           = circle,
                           shading         = ball,
                           ball color      = green!60!black,
                           minimum size    = 24pt,
                           draw]
\tikzstyle{EdgeStyle}   = [thick,%
                           double           = orange,
                           double distance  = 1pt] 
\SetVertexNoLabel
\grGeneralizedPetersen[Math,RA=5,RB=2]{5}{2}
\end{tikzpicture}
\end{center}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Heawood graph

Heawood graph : [PDF] [TEX]

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[usenames,dvipsnames,pdftex]{xcolor}
\usepackage{tkz-berge,fullpage}
\thispagestyle{empty}
\begin{document}
\begin{center}
\begin{tikzpicture}
   \tikzstyle{VertexStyle}=[shape        = circle,
                            shading      = ball,
                            ball color   = Blue!60,
                            minimum size = 24pt,
                            draw]
   \SetVertexNoLabel
   \tikzstyle{EdgeStyle}= [thick,
                           double          = orange,
                           double distance = 1pt]
   \grHeawood[RA=6]
\end{tikzpicture}
\end{center}
\end{document}
% Author : Alain Matthes
% Encoding : UTF8
% Engine : PDFLaTeX

Alain Matthes — al.ma@mac.com — last modification: « 01/03/2009 » with TextMate Hosted by WebFaction.