Global Dominator Coloring of Graphs

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Abstract

Let SV. A vertex vV 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 vV (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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Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information


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CiteScore 2017: 0.64

SCImago Journal Rank (SJR) 2017: 0.633
Source Normalized Impact per Paper (SNIP) 2017: 1.095

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Target Group

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

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