Given a graph G=(V,E) and a weight function w:E →R, a coloring of vertices of G, induced by w, is defined by χ_w(v) = ∑_e∋v w(e) for all v∈V. In this paper, we show that determining whether a particular graph has a weighting of the edges from {1,2} that induces a proper vertex coloring is NP-complete.