Geodesic
Global Dominator Coloring of Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 325-339

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Let S ⊆ V. A vertex v ∈ V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let C = (V1, V2, . . ., Vk) be a coloring of G and let v ∈ V (G). A color class Vi is called a dom-color class or an anti domcolor class of the vertex v according as v is a dominator of Vi or an antidominator of Vi. The coloring C is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti dom-color class in C. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by χgd(G). This paper initiates a study on this notion of global dominator coloring.
Keywords: global domination, coloring, global dominator coloring, dominator coloring 
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     title = {Global {Dominator} {Coloring} of {Graphs}},
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Hamid, Ismail Sahul; Rajeswari, Malairaj. Global Dominator Coloring of Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 325-339. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a2/