Geodesic
The set chromatic number of a graph
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 545-561

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For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs are determined and several bounds are established for the set chromatic number of a graph in terms of other graphical parameters.
Keywords: neighbor-distinguishing coloring, set coloring, neighborhood color set 
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Chartrand, Gary; Okamoto, Futaba; Rasmussen, Craig; Zhang, Ping. The set chromatic number of a graph. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 545-561. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a6/