Given a (non-multi)graph $G$ let $N\_G$ be the least number of nodes that must be colored (by a single color) such that every other node in $G$ shares an edge with at least one colored node. (I am only interested in the case where $G$ is an $n \times n$ grid, where such an $N\_G$ obviously always make sense - I don't know what constraints (or their names) must be put on $G$ in general for $N\_G$ to make sense, but assume 'obvious' ones.)


Is there a technical, graph-theoretic term for $N\_G$?



Name for minimum size of a set of vertices S such that every other vertex has a neighbor in S
This is the domination number of the graph. 


Here's a wikipedia article:


[en.wikipedia.org/wiki/Dominating\_set](http://en.wikipedia.org/wiki/Dominating_set)


