(*  Hopefully a critically hamiltonian graph
It is the Paley graph on a=p vertices.
*)

paley[a_] :=
Block[{p=a},
ponot = Range[0,p-1,1] ;
f[x_]=Mod[x^2,p];
generatorlist = Map[ f, Range[p-1]];
MakeGraph[ ponot,
  (
    MemberQ[generatorlist,Mod[#2-#1, p]]
  )&,Type->Undirected   ]
];