  We propose an algorithm for obtaining the common transfer digraph $ D^*_m$
for enumeration of 2-factors in graphs from the title all of which with $m n$
vertices ($m, n \in N, m >1 $).
  The numerical data gathered for $m <19$ reveal some matchings of the numbers
of 2-factors for different types of torus or Klein bottle. In latter case we
conjecture that these numbers are invariant under twisting.
