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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 $N_G$?

flag	asked Sep 6 at 19:17 Chuck 378●5●11

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

Patricia Hersh · Accepted Answer · 2012-09-06 19:26:26Z UTC

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This is the domination number of the graph.

Here's a wikipedia article:

en.wikipedia.org/wiki/Dominating_set

answered Sep 6 at 19:26

Patricia Hersh
2,705●1●10●21

	To stress the point further, this is not a coloring concept at all. – Felix Goldberg Sep 6 at 19:44
	@Felix Goldberg: good point, though perhaps he just found this to be a convenient language in which to explain his question. – Patricia Hersh Sep 6 at 20:53

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