The following is the Cayley graph \Gamma(G,S), where G is the additive group of the vector space V=F^2 (where F=\{0,1,2\} is the field of three elements), and S=\{(1,0),(2,0),(0,1),(0,2)\}. 

\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}

A Cayley graph

See also: Original Source by Rafael

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