Geodesic
Defining sets in (proper) vertex colorings of the Cartesian product of a cycle with a complete graph
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 59-72

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In a given graph G = (V,E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G, if there exists a unique extension of the colors of S to a c ≥ χ(G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G,c).
Keywords: graph coloring, defining set, cartesian product 
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Mojdeh, D. Defining sets in (proper) vertex colorings of the Cartesian product of a cycle with a complete graph. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 1, pp. 59-72. http://geodesic.mathdoc.fr/item/DMGT_2006_26_1_a5/