(*  
The Cayley graph of the group
   <a,b|a^3=b^7=1, ba=ab^2> 
(therefore elements of the form a^ib^j)
with generating set
 {a, a^{-1}, b, b^{-1}}
*)


ponot = Partition[
           Flatten[
             Table[
                {i,j}, {i,0,2}, {j,0,6}
                  ]
                 ], 2
                ] ;


cay21=MakeGraph[ ponot,
  (
    (
      (#2[[1]]==#1[[1]])&&
      (#2[[2]]==Mod[#1[[2]]+1, 7])
    )||
    (
      (#2[[1]]==#1[[1]])&&
      (#2[[2]]==Mod[#1[[2]]-1, 7])     
    )||
    (
      (#2[[1]]==Mod[#1[[1]]+1, 3])&&
      (#2[[2]]==Mod[2*#1[[2]], 7])
    )||
     (
      (#2[[1]]==Mod[#1[[1]]-1, 3])&&
      (#2[[2]]==Mod[4*#1[[2]], 7])
    )
  )&, Type->Undirected     ];