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On dominated coloring of graphs and some Nordhaus-Gaddum-type relations

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On dominated coloring of graphs and some Nordhaus-Gaddum-type relations

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The minimum number of colors needed for a dominated coloring of G is called the dominated chromatic number of G, denoted by χdom (G). In this paper, dominated coloring of graphs is compared with (open) packing number of G and it is shown that if G is a graph of order n with diam(G) ≥ 3, then χdom(G) ≤ n − ρ(G) and if ρ0(G) = 2n/3, then χdom(G) = ρ0(G).

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Nội dung Text: On dominated coloring of graphs and some Nordhaus-Gaddum-type relations

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