  Let G be a simple graph. A coloring of vertices of G is called (i) a 2-proper
coloring if vertices at distance 2 receive distinct colors; (ii) an injective
coloring if vertices possessing a common neighbor receive distinct colors;
(iii) a square coloring if vertices at distance at most 2 receive distinct
colors. In this paper, we study inequalities of Nordhaus-Guddam type for the
2-proper chromatic number, the injective chromatic number, and the square
chromatic number.
