Summary of Results of Domination Project.

1. Size of smallest Non-zero (mod k) dominating set
in n by m grid (k >= 3) is equal to size of smallest
dominating set. To prove this, one can show that there
exists a smallest dominating set for all grids such that
no vertex is dominated more than twice. Note that there exist
minimum dominating sets of some grids (e.g. 3 by 3) that do
not have this property.

2. Maximum Non-zero (mod 3) dominating set in grids generated
by this pattern (can prove this is maximum)

x x x x ...  x x
o x x x ...  o x
o x x x ...  o x
x x x x ...  x x
o x x x ...  o x
...............
x x x x ...  x x

(every third internal row is all x's).

3. Linear-time algorithm to find smallest (or largest) Non-zero
(mod k) set in a tree.

4. Number o non-zero (mod k) dominating sets found for various
grid dimensions.

5. Variations of even/odd dominating sets considered
for grids (e.g. total odd domination, open odd domination)
and programs written to test which grids have these. The
data is on the web site and a study of the data is being
undertaken.