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.
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researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs