  The secure domination numbers of the Cartesian products of two small graphs
with paths or cycles is determined, as well as for Mobius ladder graphs. Prior
to this work, in all cases where the secure domination number has been
determined, the proof has either been trivial, or has been derived from lower
bounds established by considering different forms of domination. However, the
latter mode of proof is not applicable for most graphs, including those
considered here. Hence, this work represents the first attempt to determine
secure domination numbers via the properties of secure domination itself, and
it is expected that these methods may be used to determine further results in
the future.
