Category Graph Theory in LaTeX (Rafael)

The following is the Cayley graph , where is the additive group of the vector space (where is the field of three elements), and . \begin{tikzpicture} \tikzset{VertexStyle/.style={draw,rectangle}} \grEmptyCycle*[rotation=90,prefix=a,RA=2,Math]{{(1,2)},{(0,0)},{(2,1)}} \grEmptyCycle*[rotation=90,prefix=b,RA=4.5,Math]{(2,0),(1,0),(1,1),(0,1),(0,2),(2,2)} \EdgeInGraphLoop{b}{6} \SetUpEdge[style={bend right=10}] \EdgeDoubleMod{a}{3}{0}{1}{b}{6}{1}{2}{3} \EdgeDoubleMod{a}{3}{0}{1}{b}{6}{2}{2}{3} \SetUpEdge[style={bend left=10}] \EdgeDoubleMod{a}{3}{0}{1}{b}{6}{4}{2}{3} \EdgeDoubleMod{a}{3}{0}{1}{b}{6}{5}{2}{3} \end{tikzpicture} See… Continue Reading →

The purpose of the new package graphiso.sty is to use tkz-graph to produce an animation of a graph isomorphism in a beamer presentation, such as: You can find documentation and code at Github: rvf0068/graphiso.sty. See also: Original Source by Rafael

\begin{tikzpicture} \begin{scope}[rotate=90] \grIcosahedral[form=1,RA=3,RB=1.5] \SetUpEdge[color=white,style={double=black,double distance=2pt}] \EdgeInGraphLoop{a}{6} \EdgeFromOneToSel{a}{b}{0}{1,5} \Edges(a2,b1,b3,b5,a4) \Edge(a3)(b3) \Edges(a1,b1,b5,a5) \Edges(a2,b3,a4) \end{scope} \end{tikzpicture} See also: Original Source by Rafael

This post is an update for this post from my old blog, which did not work with the newer versions of tkz-berge. The changes are: instead of \tikzstyle{every node} = [node distance=1.5cm] one now has to use the macro: \SetGraphUnit{1.5},… Continue Reading →

For drawing some extra edges in a grid I used the following code: \begin{tikzpicture} \newcounter{xp} \newcounter{yp} \grGrid[prefix=a,RA=2,RB=2]{6}{6} \foreach \x in {0,2,4}{% \foreach \y in {1,3}{% \setcounter{xp}{\x} \setcounter{yp}{\y} \stepcounter{xp} \stepcounter{yp} \Edge(a\x;\y)(a\thexp;\theyp) } } \end{tikzpicture} For some reason the following code does… Continue Reading →

I’m using the new rotation option for cycles to define a macro that draws a flower snark. The macro has as optional arguments the radius RA, RB, and RC of the three types of vertices, and a mandatory argument which… Continue Reading →

\grEmptyCycle and \grCycle can also have options x and y, that set the coordinates of the center of the cycle, or r and d for polar coordinates (r is the radius and d the angle). Here we use these options… Continue Reading →

Finally, the much expected new versions (1.00 c) of tzk-graph and tkz-berge were released by Alain Matthes last week, and can be downloaded from Altermundus download zone. I expect to post several examples using the new capabilities of the packages…. Continue Reading →

The vertices that tkz-berge draws are regular named TikZ nodes, and so they can be used if one wants unusual edges. Update: I added four more lines, to show that one can also use the node names provided by tkz-berge,… Continue Reading →

The macro \EdgeDoubleMod is convenient when drawing some complicated graphs. Consider the following picture of the line graph of the Petersen graph. produced by: \begin{tikzpicture} \SetVertexNormal[MinSize=12pt] \tikzset{VertexStyle/.append style= {inner sep=0pt,font=\footnotesize\sffamily}} \begin{scope}[rotate=-90] \grCirculant[RA=0.6,prefix=a]{5}{2} \end{scope} \begin{scope}[rotate=-18] \grEmptyCycle[RA=1.5,prefix=b]{5}{2} \end{scope} \begin{scope}[rotate=18] \grCycle[RA=2.5,prefix=c]{5} \end{scope} \EdgeIdentity{a}{b}{5}… Continue Reading →

… after the example in the tikz gallery. \usetikzlibrary{calc,3d}\newcommand{\setxyz}[1]{% \pgfmathsetmacro{\xone}{cos(180+#1)}% \pgfmathsetmacro{\yone}{sin(180+#1)}% \pgfmathsetmacro{\xtwo}{cos(360-#1)}% \pgfmathsetmacro{\ytwo}{sin(360-#1)}%}\setxyz{17}\begin{tikzpicture}% [x = {(\xone cm,\yone cm)}, y = {(\xtwo cm,\ytwo cm)}, z = {(0cm,1cm)}] \GraphInit[vstyle=Shade] \SetVertexNoLabel \begin{scope}[canvas is xy plane at z=-5] \Vertex{x} \end{scope} \begin{scope}[canvas is xy plane… Continue Reading →

This is the circulant C_9(1,2,3,4)\begin{tikzpicture}\usepgflibrary{arrows}\GraphInit[vstyle=Art]\SetUpEdge[style={->,>=angle 45,bend right=10},color=red]\grCirculant[RA=3]{9}{1,-2,3,-4}\end{tikzpicture} See also: Original Source by Rafael

UPDATE: This example no longer works with the latest versions of tkz-graph and tkz-berge. For an updated version see this post at my new blog. \begin{tikzpicture}\SetVertexNormal[LineColor=brown]\Vertex[x=0,y=2.5,style=orange,LabelOut=true,Lpos=90]{A}{\tikzstyle{every node} = [node distance=1.5cm] \Vertices[x=1.5,y=4,dir=\SO,LabelOut=true,Ldist=5pt]{B,C,D}}\Vertices[x=3,y=5,dir=\SO,style={shape=coordinate}]{E,F,G,H,I,J}\Vertices[x=4.5,y=5,dir=\SO,style={font=\bfseries}]{K,L,M,N,O,P}{\tikzstyle{every node} = [node distance=1.5cm] \Vertices[x=6,y=4,dir=\SO, style={line width=2pt, inner sep=0pt,… Continue Reading →

\begin{tikzpicture} \SetVertexNormal \Vertex[x=0,y=2.5]{A} {\tikzstyle{every node} = [node distance=1.5cm] \Vertices[x=1.5,y=4,dir=\SO]{B,C,D}} \Vertices[x=3,y=5,dir=\SO]{E,F,G,H,I,J} \Vertices[x=4.5,y=5,dir=\SO]{K,L,M,N,O,P} {\tikzstyle{every node} = [node distance=1.5cm] \Vertices[x=6,y=4,dir=\SO]{Q,R,S}} \Vertex[x=7.5,y=2.5]{T} \Edges[color=red](A,B,E,K,Q,T,S,P,J,D,A) \foreach \x/\y in {E/F,G/H,I/J,K/L,M/N,O/P} {\Edge[color=green](\x)(\y)} \Edge[style=->](I)(P) \Edge[style=dashed](A)(C) \Edge[style=dotted](C)(F) \Edge[label=CD](C)(D) \Edge[label=BC,labelcolor=yellow](B)(C) \Edge[label=QR,labelcolor=orange,labeltext=cyan](Q)(R) \Edge[label=RS,labelstyle=right](R)(S) \Edge[label=OS,labelstyle={below=1pt,inner sep=0pt}](O)(S) \Edge[label=LQ,labelstyle={above,font=\bfseries}](L)(Q) \Edge[label=FL,labelstyle={font=\tiny\bfseries}](F)(L) \Edge[label=GN,labelstyle={sloped,above}](G)(N) \Edge[style={bend right}](A)(T)\end{tikzpicture} See also:… Continue Reading →

I stumbled upon a piece of software called KtikZ. The screenshot in that page, together with the fact that Doc-View mode is included in the new Emacs 23, inspired me to try that idea with tikz2pdf. With help from folks… Continue Reading →

Alain Matthes has produced a package (tkz-berge.sty) which should become THE way to draw graphs in LaTeX. It is built on top of Tikz, and so can be easily integrated with beamer presentations. The package can be dowloaded from here,… Continue Reading →

See this paper \documentclass{article}\usepackage{tikz}\pagestyle{empty} \begin{document}\begin{center} \begin{tikzpicture}[style=thick] \foreach \x in {18,90,…,306} { \draw (\x:4cm) circle (2pt) — (\x+72:4cm); \draw (\x:4cm) — (\x:3cm) circle (2pt); \draw (\x:3cm) — (\x+15:2cm) circle (2pt); \draw (\x:3cm) — (\x-15:2cm) circle (2pt); \draw (\x+15:2cm) — (\x+144-15:2cm); \draw… Continue Reading →

See this paper. \documentclass{article}\usepackage{tikz}\pagestyle{empty} \begin{document}\begin{center} \begin{tikzpicture}[style=thick] \foreach \x in {0,30,…,330} { \draw (\x:2cm) circle (2pt) — (\x+30:2cm); } \foreach \x in {0,60,…,300} { \draw (\x:2cm) circle (2pt) — (\x+90:2cm); } \foreach \x in {0,30,…,150} { \draw (\x:2cm) circle (2pt) —… Continue Reading →

\documentclass{article}\usepackage{tikz}\pagestyle{empty} \begin{document}\begin{center} \begin{tikzpicture}[style=thick] \foreach \x in {0,15,…,345} { \draw (\x:3cm) circle (2pt) — (\x+15:3cm); } \foreach \x in {0,45,…,135} { \draw (\x:3cm) circle (2pt) — (\x+180:3cm); } \foreach \x in {15,60,…,330} { \draw (\x:3cm) circle (2pt) — (\x+105:3cm); } \end{tikzpicture}\end{center}\end{document}… Continue Reading →

\documentclass{article} \pagestyle{empty}\usepackage{tikz} \begin{document} \begin{center} \begin{tikzpicture}[style=thick,scale=0.5] \def\pentagon{(18:1cm) circle (4pt) node[above right=-1.75pt]{\tiny $4$} — (90:1cm) circle (4pt) node[above]{\tiny $0$} — (162:1cm) circle (4pt) node[above left=-1.75pt]{\tiny $1$} — (234:1cm) circle (4pt) node[below]{\tiny $2$} — (306:1cm) circle (4pt) node[below]{\tiny $3$} — (18:1cm)} \def\pentagram{(18:1cm) circle… Continue Reading →

The unique smallest cubic graph of girth 8. Drawn from Algebraic Graph Theory by Godsil and Royle, p.72. \documentclass{article}\usepackage{tikz}\pagestyle{empty} \begin{document}\begin{tikzpicture}[style=thick] \foreach \x in {0,36,…,324} { \draw (\x:2cm) circle (2pt) — (\x+144:2cm); \draw (\x-10:3cm) circle (2pt) — (\x+5:4cm); \draw (\x-10:3cm) circle… Continue Reading →

\documentclass{article}\usepackage{tikz}\pagestyle{empty} \begin{document} \begin{center} \begin{tikzpicture}[style=thick] \foreach \x in {0,1,2} \foreach \y in {0,1,2} {\draw (\y,0) — (\x,1);} \foreach \x in {0,1,2}{ \draw (\x,0) circle (2pt); \draw (\x,1) circle (2pt);} \end{tikzpicture} \end{center}\end{document} See also: Original Source by Rafael

If it could be completed to a cubic graph, it would give a cubic Moore graph of diameter 3. I wish I knew how to produce a similar tree, but growing from an edge instead of from a vertex.\documentclass{article} \usepackage{tikz}… Continue Reading →

The smallest cubic graph of girth 5, drawn using TikZ. \documentclass{article}\usepackage{tikz}\pagestyle{empty} \begin{document} \begin{center} \begin{tikzpicture}[style=thick] \draw (18:2cm) — (90:2cm) — (162:2cm) — (234:2cm) — (306:2cm) — cycle; \draw (18:1cm) — (162:1cm) — (306:1cm) — (90:1cm) — (234:1cm) — cycle; \foreach \x… Continue Reading →

The smallest cubic graph of girth 6, or 6-cage, drawn with PS Tricks. This was inspired from the example in The LaTeX Graphics Companion, page 121. \documentclass{article}\usepackage{pstricks,pst-node,multido,ifthen,calc}\pagestyle{empty} \begin{document}\begin{center}\begin{pspicture}(-1,-1.5)(1,1.5) \psset{unit=1.5cm} \newcounter{CtA} \newcounter{Temp} \newcounter{Tempi} \SpecialCoor \degrees[14] \multido{\ia=0+1}{14}{% \setcounter{CtA}{\ia}% \addtocounter{CtA}{1}% \multido{\ib=\value{CtA}+1}{1}{\psline{o-o}(1;\ia)(1;\ib)} }% \multido{\ia=0+2}{7}{%… Continue Reading →