A dominating set in a graph is a subset of vertices D such
that every vertex in the graph is either in D or adjacent to
at least one element of D. Dominating sets are one of the most widely 
studied concepts in graph theory and have many applications in computing.
The focus of the proposed project is on a general form of domination in 
which each vertex in the graph is required to be adjacent (not adjacent)
to a certain number of vertices in the dominating (not in the dominating
set). In particular, we are interested in the case when the number of 
neighbors each vertex has in D must satisfy a parity-type constraint 
(e.g., be even, or be odd and also be such that the subgraph induced 
by D be connected). We will consider which graphs have these sets and 
if a graph does have such a set, the number and sizes of these dominating 
sets. Much of the work will involve writing computer programs to evaluate
numerous graphs and subsequent data analysis. This work is a continuation
of an ongoing project that began with an analysis of the computer game 
"Lights Out!"