Graph Theory Terminology Question

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 $n$x$n$ 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 $N_G$?

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I definitely wouldn't tag the question "graph-colorings." –  Douglas Zare Sep 7 '12 at 5:30