JohnsonGraph:=function(v,k)
 G:=Sym(v);
 X:={@ s : s in Subsets({1..v},k) @};
 H:=StandardGroup(ActionImage(G,GSet(G,X))); 
 t:=exists(i){ j : j in [1..#X] | #(X[1] meet X[j]) eq k-1 };
 return OrbitalGraph(H,1,{i});
end function;